Questions related to real and complex logarithms.

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0answers
15 views

How to steepen logarithmic function without reducing constant of deceleration

As you can see I have plotted my points in Geogebra and compared them to the function $ y=log_{10}x $ They clearly don't coincide, how would I go about adjusting the function in order to find the ...
3
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1answer
30 views

Prove convergence of this generalized integral

Prove the convergence of $$\int_0^1 \left[\ln\left(1+\frac1x\right)\right]^a\mathrm dx$$ for $ a>0$.
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2answers
71 views

Compute $\lim\limits_{n\to \infty} \ln(3n+7) - \ln(n)$

The reason why I'm having trouble with this problem is because it involves natural log (ln) and I need to find the limit. I need to find $\lim_{n\to\infty} \ln(3n+7)-\ln(n)$. I noticed that as $n$ ...
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2answers
54 views

Solve the logarithmic equation by $x$

Solve the eqation for all real $x$: $\log_2(x^2+7)+\log_3(x+6)=6$. What I tried: $\log_2(x^2+7)=a$ and $\log_3(x+6)=b$, then $a+b=6$ and $2^a=3^{2b}-4\cdot3^{b+1}+43$. But the problem is $a$ and $b$ ...
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2answers
73 views

Solving for n, n is an exponent.

If you have a sequence of random numbers ranging between 1 and 64, what is the length of a sequence that will give a 98% chance of having at least one ( 1, 2, or 3) in the sequence? Here is ...
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1answer
20 views

Multi-variable calculus involving $\ln$

I am having difficulty with differentiating this equation with respect to $y$: $$ W= x^{y \ln(z)}. $$ Differentiating calculators are giving me the answer $$\ln(x) \ln(z).x^{y \ln(z)}$$ But I ...
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1answer
31 views

Is it true that $x^n <\epsilon \Rightarrow n < \frac{\ln \epsilon}{\ln x}$?

Let: $0 \lt x \lt 1$ $\epsilon > 0$ I need to show that there exists an $N(\epsilon,x)$ such that: $n\ge N(\epsilon,x) \Rightarrow x^n < \epsilon$ This is what I've tried: $x^n ...
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1answer
30 views

How to “see” that this expression is $>0$.

$N \in \mathbb N$. $\displaystyle\int_{N-1}^N \left(\dfrac{1}{x} - \dfrac{1}{N}\right) dx>0$ This is the finish of a proof, a modification of $\log N-\log (N-1) -\frac{1}{N}$. Calculating it ...
4
votes
2answers
48 views

If $\log_{12}54=a$ then $ \log_{6}12=?$

I am given $$\log_{12}54=a$$ So what will be value of $ \log_{6}12?$ I used base changing theorem and wrote expression as $$\frac{\log_{6}54}{ \log_{6}12} =a$$ And then $$ \frac{1+\log_{6}9}{ a} = ...
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1answer
31 views

How to solve equations containing logarithms and exponentials

Equation 1: $x+e=e^x$ According to Wolfram alpha : Solution of x $\approx$ -2.6 and 1.4 Equation 2: $x-e = \ln(x)$ According to wolfram alpha, Solution for x $\approx$ 0.07 and 4.1 How does ...
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1answer
16 views

Properties of Geometric Series

If we have a geometric series $(x_1, x_2, ..., x_{n-1}, x_{n})$ of reason $q$, we can determine the general term formula to be: $x_{1}q^{n-1} = x_{n}$ But by taking the logarithm of the equation we ...
0
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0answers
11 views

Linking summations with their correct function(s)

Guys can you please guide me step by step on how to link given functions with the functions to choose from. So for example a function $g(n)\in \Theta n^2$ and if there is no match then you say there ...
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vote
4answers
63 views

If $a^x=b$, then $ x=$?

Stupid question, I know, but I couldn't remember nor find information by googling on how to find the exponent of $a$ that gives $b$ as the result. If $a^x=b$, then $x=log_a b$ but how do you find $x$? ...
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4answers
80 views

How to determine the monthly interest rate from an annual interest rate

I have a calculation which gives me the annual interest rate if I already know the monthly interest rate as follows: (Monthly interest rate + 1)^12 In this case I ...
2
votes
2answers
40 views

Solving inequality involving square root and division by logarithm.

I would like to solve the inequality $\sqrt n<\frac{n}{\log(n)}-2$. for some reason I had never done this before. This is clearly the same as $\frac{n}{\log(n)}-\frac{n}{\sqrt{n}}>2$. Which is ...
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0answers
23 views

Homework : Anti log expression

I have this expression $x(r) = y(a)r^a$ where $r$ is a random variable and I want to express the expression in terms of $r$. The objective is to substitute the variable $r$ into the pdf of $r$, ...
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1answer
41 views

Solving natural logarithms with absolute value

Question from my text: $e^{4x-2014} - 7 = |-3|$. I've never seen this before and my text is useless! Thank you!
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0answers
22 views

Notation question

What exactly do you think $\ln^rn$ means in this context? "Prove that the relation $\tau(n) = O(\ln^rn)$ is false for all fixed powers $r$." Where $\tau$ is the divisor function.
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1answer
17 views

Log inequality- is $(\lceil\log x\rceil - \lfloor\log m\rfloor)\cdot m+2^{\lfloor\log m\rfloor+1}\leq m\cdot(\lceil\log\frac{x}{m}\rceil+2)$?

I'm having some hard times making a tight analysis of the memory requirements for my algorithm. I want to show the following inequality, which will show my data structure can use about 2 bits per ...
2
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2answers
45 views

Log inequality - is $\lceil\log x\rceil - \lfloor\log y\rfloor\leq \lceil\log\frac{x}{y}\rceil+1$

Is it true that $$\forall x>y\in\mathbb N:\lceil\log_2 x\rceil - \left\lfloor\log_2 y\right\rfloor\leq \left\lceil\log_2\frac{x}{y}\right\rceil+1$$? I reached this inequality when further ...
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2answers
42 views

properties of logarithms ln12-ln2=ln6

I checked wolframalpha and it says that ln12-ln2=ln6. How? i tried to do: ln12=ln(2*2*3) which may be 2ln(2*3) (which is probably wrong). I need help. EDIT: Ok, thanks. Actually i could have just ...
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1answer
24 views

Inverse a simple equation

Consider equation $y = x\cdot 2^x$ Can you write $x$ based on $y$ ? Is it possible ? Thanks
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3answers
28 views

Given $\log_3 x –\log_3(x – 5) = \log_3 A$, express $A$ in terms of $x$ [closed]

Given that $\log_3 x –\log_3(x – 5) = \log_3 A$, express $A$ in terms of $x$. I kinda get it.. but I'm stuck what its trying to say. Please can you show me the working out so I can understand it, ...
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4answers
35 views

using logarithms to solve the following equation to find x

$9^{2x} = 27^{1-x}$ ?? I'm really struggling with this questions. I appreciate your help and if you can please show me your working out so I can understand it too,
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2answers
49 views

formula for logarithmic spiral on a linear level

I am trying to plot the contents of a circle, which include geometric elements and spirals, on a linear graph. For example, take a circle, take the beginning and the end and make it straight. What ...
0
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1answer
44 views

Summation of harmonic series. [closed]

I'm trying to figure out how to answer this linear algebra question and can't figure it out. Can someone please explain it to me? Thanks a bunch! Here's the questions:
4
votes
4answers
107 views

Weird integration issue: $\ln(x+1)=\ln(2x+2)$ ?!

Weird integration issue: Using $(\ln[f(x)])'=\frac {f'(x)}{f(x)}$ we get that $\int \frac{2\,dx}{2x+2}=\ln(2x+2)$. Yet, $\int \frac{2\,dx}{2x+2}= \int\frac{dx}{x+1}=\ln(x+1)$ using the same rule as ...
2
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2answers
66 views

Does there exist any positive integer $n$ such that $e^n$ is an integer (to show $\log 2$ is irrational)?

Does there exist any positive integer $n$ such that $e^n$ is an integer ? I was in particular trying to prove $\log 2$ is irrational; now if it is rational, then there are relatively prime ...
2
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1answer
30 views

Deriving logarithm in exponent

Im attempting to take the derivative of $n^{log_2(n)}$, but the answer I'm getting is different from http://www.derivative-calculator.net/.. this isnt highschool math homework, I'm trying to use ...
3
votes
3answers
66 views

What $n^{\frac{1}{\log_2n}}$ means?

I was confused with about the $n^{\frac{1}{\log_2n}}$ expression. I am not sure how to make mathematical sense of it - i.e. express it in another way for easier understanding. I tried to plug in some ...
1
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1answer
41 views

$a$ has a square root modulo $p$ if and only if its discrete logarithm log$_{g}(a)$ modulo $p - 1$ is even

Questions: Let $p$ be an odd prime and let $g$ be a primitive root modulo $p$. Prove that $a$ has a square root modulo $p$ if and only if its discrete logarithm log$_{g}(a)$ modulo $p - 1$ is even. ...
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4answers
80 views

How to find $x$ in the equation $a=b^x$? [closed]

I need to know how to solve this equation for $x$. $a=b^x$
2
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2answers
193 views

Solving a second-degree exponential equation with logarithms

The following equation is given: $8^{2x} + 8^{x} - 20 = 0$ The objective is to solve for $x$ in terms of the natural logarithm $ln$. I approach as follows: $\log_8{(8^{2x})} = \log_8{(-8^{x} + ...
1
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1answer
41 views

How to simplify logs and powers?

Is there any way to simplify $(\log a)^{\log b} = c$? And even this $(\log x)^y = z$? And also this $(\log m)(\log n) = p$ (which is essentially $\log m^{\log n} = p$) I was trying to simplify some ...
5
votes
4answers
148 views

Can someone explain why $x^{\log(a)} = a^{\log(x)}$?

I'm trying to see why the below is true. $$ x^{\log(a)} = a^{\log(x)} $$ Anyone here know why this is? Thank you.
0
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4answers
106 views

Does $\ln|x+2|=\ln|2x+4|$ and if so why so? [closed]

Is $\ln|x+2|=\ln|2x+4|$? Is this right? I saw something earlier saying this was correct; my first instinct was no.
2
votes
1answer
21 views

how to calculate this logarithmic function?

Im having trouble in graphing this log function: $y=\log _{1/4}\left|x^2-5x+6\right|$ I found the intervals: $(-\infty, 2)$, $(2,3)$, $(3,\infty)$ Should I just give $x$ values and find $y$ to graph ...
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2answers
39 views

Find the general expression from the antiderivative

I am having trouble computing the original function. Question states: Let $f$ be a differentiable, positive function, such that $$f'(x)=x*f(x)$$ for all real numbers x. A) Find the general ...
0
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1answer
25 views

Confusion: dB to scalar and from scalar to dB

Assume we have $$N_1=5 \text{ dB}$$ $$N_2= - 110 \text{ dB}$$ Then we have $$Y=N_1+N_2=-105 \text{ dB} $$ If I convert to scalar then $$10 \log(X) = -105 \rightarrow X=10^{-10.5}$$ Let me start the ...
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1answer
46 views

Solving a ln divided by a ln.

I am having trouble figuring out how to calculate this. Thank you for your help. $$.926 = \frac{ln(1+.8u)}{ln(1+u)}$$ What does $u$ equal?
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0answers
24 views

Standard deviation errors in log scale

I have a not so common issue with error bars in the log log scale. To be more precise, I have measurements of a quantity Y with an associated standard error Yer that has normal distribution and these ...
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1answer
30 views

How do you simplify this logarithm?

$$\large\log\sqrt[3]{\frac{x^2y^5}{z}}$$ I think this is the answer, but I'm not positive:$$\frac{1}{3}\left((2\log{x}+5\log{y})-(\log{z})\right)$$
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1answer
25 views

Need help with understanding manipulations on logarithms

I cannot understand the result from logarithms manipulations even though I am going over logarithmic properties. I am simply stuck. So here is the problem: $$n = 2^k \implies k = \log_2n$$ $$x = 3^k ...
2
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1answer
53 views

How to show without calculator that $\left\lfloor\, \log_{10}{999^{999}}\right\rfloor =\left\lfloor\, \log_{10}{999^{999}}+\log_{10}2\right\rfloor$

By wolfram alpha, I get $\left\lfloor\, \log_{10}{999^{999}}\right\rfloor =\left\lfloor\, \log_{10}{999^{999}}+\log_{10}2\right\rfloor=2996$. How to prove that $\left\lfloor\, ...
0
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1answer
73 views

Why is -ln x is not equal to 1/ln x?

I am doing differential equation now and I need to convert them into the proper form in order to do my homogeneous differential equation. So now I just found out that -ln x is not equal to 1 / ln x. I ...
0
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1answer
28 views

Solutions to $N=2^r-r-1$

Considering this equation $N=2^r-r-1, N \in \mathbb{N},r \in \mathbb{N}$. I've tried (unsuccesfully) working out $r$ given $N$. However I recently stumbled across a website which was using $\left ...
0
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1answer
17 views

Unique intersection of $b^x$ and $\log_b(x)$

It seems to me that there is exactly one real number $b>1$ such that the graphs of $y=b^x$ and $y=\log_b(x)$ intersect at a single point. What exactly is this number?
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3answers
89 views

Limit of logarithms exponential

$$ \lim_{x\to\infty}\biggl(\frac{\ln(x-2)}{\ln(x-1)}\biggr)^{x\ln x}. $$ L'Hopital seems like a very hardcore solutions given the situation.Are the any other options?
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7answers
62 views

Logarithms with an answer that is a fraction

How does log base $16$ of $32$ equal $1.25$? If we divide $32/16=2$ but then if we divide $2/16$ it doesn't come out to a whole number unlike with log base $2$ of $4$ where $4/2=2$ and $2/2=1$ I am ...
2
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0answers
26 views

Taking logs multiple times

Is there a formule to calculate (log (log ( log ... log n))) assume all the base to be the same (b)? I was not able to find one on wikipedia.