Questions related to real and complex logarithms.

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-5
votes
2answers
31 views

Calculating log 2274,207,281,512 in base 10. [on hold]

Can log 2^274,207,281,512 in base 512 be calculated?
0
votes
1answer
20 views

Complex numbers: find all $z$ such that $e^{z-2}=-ie^2$

Ok, so I think I'm getting the hang of this. Is this more or less on the right track? $$e^{z-2}=-ie^2$$ $$e^ze^{-2}=-ie^2$$ $$e^z=-ie^4$$ $$\ln(e^z)=\ln(-ie^4)$$ $$z=\ln|-i|+iarg(-i)+2\pi ik+4$$ ...
2
votes
2answers
52 views

What is the value of $\log_b m^{\log_b n}$?

What is the value of the following expression? $$\log_b \left( m^{\log_b n} \right)$$ As far as I know it should be: $$\log_bn\;\times\;\log_bm$$ Can it be simplified further? If so how? ...
1
vote
2answers
23 views

Analyze the Complex Function by using the Principal log Branch

I am trying to analyze the function $\sqrt{1-z^2}$, where the square root function is defined by the principal branch of the log function. I want to locate the the discontinuities. I know the ...
0
votes
0answers
69 views

The domain of $\frac{\ln x}{x}$.

I have to find the domain for $f(x) = \frac{\ln x}{x}$ Naturally, $x$ must be larger than $0$ and $x$ can't be $0$ so $x > 0$. But when I graphed the function, it has two "parts", one in the ...
-1
votes
2answers
69 views

To evaluate $\lim_{x \to 0^+} \frac{\log(x)}{\sqrt x}$ using inequality [on hold]

To evaluate $$\lim_{x \to 0^+} \frac{\log(x)}{\sqrt x}$$ I know that $\log(x) < x$ for $x > 0$. So dividing by square root of $x$ and taking limits gives me nothing. Which inequality should I ...
0
votes
1answer
24 views

Is $\log (t^2 (l/c)) = \log (t^2) \log (l/c)$?

I'm new in this forum want to ask a beginner question about logarithm: Is $\log (t^2 (l/c)) = \log (t^2) \log (l/c)$?
0
votes
0answers
23 views

Help with understanding when Log(z^k)=k Log(z) as well as drawing the function.

For the question I'm dealing with the property Log(z^k)=k*Log(z)in which I have to find the largest open set that this property is true when $k$ is a positive integer. I understand that this ...
3
votes
0answers
56 views

Want to know what's wrong?

I take a exercise from apostol's book. I was trying the next exercise and do it, but the answer (from the book) is different, and I don't know what part of my procedure it's wrong?. So I want to know ...
2
votes
2answers
34 views

Is there an alternative approach to the definition of prime numbers based on the definition of the natural logarithm?

Is there an alternative approach to the definition of prime numbers based on the definition of the natural logarithm? These are my thoughts about it, the questions are at the end: Basically when a ...
0
votes
0answers
11 views

how would zipf's law be expressed as a logarithmic function?

I am doing a project for math class based on Zipf's law but i cannot understand how it relates to logarithms. The project handout states that "In 1949, George Zipf noticed that if you tabulate the ...
-1
votes
1answer
48 views

How do I solve logarithms with addition in them? [on hold]

I've asked wolfram alpha to see if there is any solution and in fact there is. Now I just need a way to do this by hand because my school wants me to know such things. So I would really appreciate any ...
1
vote
4answers
53 views

Find the limit of fraction involving logarithms

I am looking for a way to prove the following limit for integer $x$s: $$\lim_{x\to\infty}{\frac{\log(x+2)-\log(x+1)}{\log(x+2)-\log(x)}}=\frac{1}{2}$$ I could find the result by using a computer ...
0
votes
2answers
30 views

Expanding logarithm of function

Is there a way (there has to be), I can expand an expression like this? $$\log_2 (3f(n)^n)$$ P.S. This part of an assignment I'm working on, please do not give solutions
1
vote
2answers
41 views

Find all $x$ such that $8^x(3x+1)=4$

Find all $x$ such that $8^x(3x+1)=4$,and prove that you have found all values of $x$ that satisfy this equation. My effort Rewriting the equation I have \begin{array} 22^{3x}(3x+1)&=2^2 \\ ...
-4
votes
0answers
55 views

solve $4x^2y'' + y=0$, $y(-1)=2, y'(-1)=4$

This would require taking the $\ln(-1)$, which Zill solved in the 7th edition of diff eq $4.7$ problem $37$ by substituting $t$ for $x, y(1)=2, y'(1)=4$. Then substituting $-x$ for $t$ in the final ...
2
votes
2answers
29 views

How to express $\log_5 2$ in terms of a and b (Refer to qn)

In my textbook, I came across this interesting question which I am currently struggling to solve: If $\log_6 2 = a$ and $\log_5 3 = b$, express $\log_5 2$ in terms of a and b The solution given is ...
0
votes
1answer
32 views

Prove that $\sum_{i=0}^{k} \lg \frac{n}{2^i} = \Theta(\lg^2 n)$

Show that if $n$ is a power of $2$, say $n = 2^k$, then we have the equality $\sum_{i=0}^{k} \lg \frac{n}{2^i} = \Theta(\lg^2 n)$. The first step is to prove $O(\lg^2n)$: $$ \lg \frac{2^k}{2^0} + \lg ...
1
vote
3answers
63 views

Prove $\ln x \ge \frac{x-1}{x}$

Prove that for every $x>0$: $$\ln x \ge \frac{x-1}{x}$$ What I did: $$f(x) = \ln x, \text{ } g(x) = \frac{x-1}{x} $$ $$f(1) = g(1) = 0 $$ So it's enough to prove that $$ f'(x) \ge g'(x)$$ ...
4
votes
3answers
436 views

Find root of the equation

Find maximum root of the equation $$x - \frac{1000}{\log 2} \log x = 0$$ It locates between $13746$ and $13747$, but I want to find right solution not using graphing calculators. Thanks in advance.
0
votes
5answers
44 views

Equation $\log(x^2+2ax)=\log(4x-4a-13)$ has only one solution; then exhaustive set of values of $a$ is

Equation: $$\log(x^2+2ax)=\log(4x-4a-13)$$ It has only one solution; then exhaustive set of values of $a$ is ?? I don't even know where to begin The answer is : $$(-13/4,-13/12) \cup [-1]$$
5
votes
7answers
204 views

Prove that $\frac{7}{12}<\ln 2<\frac{5}{6}$ using real analysis

I studying in Real Analysis 2, but I have no idea how to solve this problem. My guess is to use Mean Value Theorem or a similar theorem? Could any one help me? Thanks.
0
votes
1answer
26 views

Solving for numerator in equation with logarithms (Activation Energy Equation)

I'm having trouble solving for k1 in this equation: ln(0.286/k1) = (100000/8.314)(1/500 - 1/490) The right side should equal 0.491, which I can calculate just fine, but then the left side gives me ...
0
votes
1answer
29 views

Converting equation to slope-intercept form

It's been awhile since I've worked problems like these and I am a bit hazy on some of the rules. I was hoping someone could show me how these are solved so that I can make sure I'm on the right path: ...
4
votes
1answer
199 views

Proof that $\frac{2}{3} < \log(2) < \frac{7}{10}$

Positive integrals $$\int_{0}^{1}\frac{2x(1-x)^2}{1+x^2}dx=\pi-3$$ and $$\int_0^1\frac{x^4(1-x)^4}{1+x^2}dx=\frac{22}{7}-\pi $$ (http://math.stackexchange.com/a/1618454/134791) prove that ...
0
votes
2answers
25 views

Most logical thing to do with these exponents and sums?

I'm doing homework for a programming class and came across this problem. There's no directions besides what I've shown, so I don't even know what it's asking me to do. What makes the most sense for ...
1
vote
1answer
40 views

Closed-form Solution of Log Sum

I have the series: $$\sum_{i=1}^{i=10^N} \log_5 i$$ I'm trying to figure out how to get the closed-form solution to this problem. I entered it into WolframAlpha and got that it equals: $ ...
0
votes
0answers
9 views

Calculating Data Rate using Quadrature Amplitude Modulation (QAM)

I was working on my telecommunications homework and I have these questions: Calculate the data rate for a 2400 baud signal where each symbol can take on one of two levels (M=2) Calculate the data ...
0
votes
1answer
24 views

solve and skecth $\log{|z|}=-2\arg(z)$

Ive asked this question a week ago, but nobody managed to answer but it is doing my heading from then. I know usually You demand some initial work done on the question but I just dont know how to ...
4
votes
1answer
73 views

How to solve $\ln(y)=\ln(x)e^{\ln(x+1)} $ for x?

I know that if I have had $y = x^{x+0} $ aka $y = x^x$ I could do $y = x^x$ // $x = e^{\ln(x)}$ $y=x^{e^{\ln(x)}}$ // $\ln$() $\ln(y) = \ln(x)e^{\ln(x)}$ then using Lambert's W function I ...
0
votes
3answers
62 views

$\frac{\ln(x^2)}{\ln(x)} = 2$? Why?

$\frac{\ln(x^2)}{\ln(x)} = 2$? Upon trying to evaluate $\frac{\ln(x^2)}{\ln(x)}$, i've found that google plots it as always equal to 2, other than 0 where it is undefined. Why is this the case?
0
votes
2answers
27 views

Solving an exponential equation with x as a base and an exponent

So here's the problem: $x+3=3^x$ Obviously, graphing both sides and finding the intersection would reveal the answer, but algebraically, how can this be solved?
0
votes
0answers
22 views

Logarithmic function transformations

The standard log function form is $a \log[k(x-d)] + c$ Where $a$ vertically stretches or compresses $k$ horizontally stretches or compresses $d$ translates left or right $c$ translates up or ...
1
vote
1answer
53 views

How do you differentiate the integral from $ \int_{e^{-x}}^{e^x} \sqrt{1+t^2}\,dt$ [duplicate]

How do you differentiate the integral from $e^{-x}$ to $e^x$ of $\sqrt(1+t^2)$ with respect to t? $$ \int_{e^{-x}}^{e^x} \sqrt{1+t^2}\,dt $$ I know the answer is $$ e^x\sqrt{1+e^{2x}} + ...
0
votes
1answer
42 views

Does $\log_2 \sqrt[4]4$ exist?

Tomorrow I have an exam about graphics and log operations. Our teacher gave us a paper with exercises to practice and one of the exercises is: $\log_2 \sqrt[4]4$ I couldn't find the solution. ...
1
vote
2answers
32 views

Order of growth of logarithms, compared to linear

I think it is true that any power of a logarithm, no matter how big, will eventually grow slower than a linear function with positive slope. Is it true that for any exponent $m>0$ (no matter how ...
2
votes
2answers
34 views

Solve for $x\quad \log_2(2^n) = \log_2(1+x)$

I am out of practice with logs, but this is derived from the channel capacity theorem. $$B\log_2\left(1 + \frac SN\right)$$ Solve for $x $ $$\log_2(2^n) = \log_2(1+x)$$ I need this equation ...
0
votes
3answers
114 views

Exponential (to the power of a logarithm) [closed]

How do I solve the following equation: $(3x)^{ln3}=(4x)^{ln4}$ Thanks in advance!
1
vote
1answer
34 views

Derivative of matrix logarithm with respect to matrix

I saw in this post that $\frac{d}{dt}\text{logm}(Z(t)) = \frac{dZ(t)}{dt}(Z(t))^{-1}$ Is this true to say: $\frac{d}{{dU}}{\mathop{\rm logm}\nolimits} (A) = {A^{ - 1}}\frac{d}{{dU}}A$ where U is ...
0
votes
2answers
25 views

Difficulty finding the sum of a hyperbolic function.

Can someone please point out where I am (If I am) going wrong during the solution process of the following question: I have been presented with the following : $$4sinh(2ln(2))-cosh(ln2)$$ and told ...
1
vote
2answers
43 views

taking the natural log of e^(2x) = (4/3)

I have been unable to answer the following question. I must solve for x: $$e^{2x} = (4/3)$$ I have been made aware that I must take the natural log of both sides, giving: $$ln(e^{2x}) = ln(4/3)$$ ...
1
vote
2answers
86 views

Use $\log(x)$ to calculate $\log(x+1)$

Given that I know the value of $\log(x)$, I would like to calculate the value of $\log(x+1)$ on a computer. I know that I could use the Taylor expansion of $\log(1+x)$, but that uses $x$ rather than ...
-1
votes
1answer
16 views

Logspace() in Matlab [closed]

In Matlab , Logspace() Generate logarithmically spaced vector . But what do we mean by them ? Earlier , I used to think that they are just equal spaced and their 10th power is returned . Like here : ...
0
votes
3answers
54 views

Show that $\frac{1}{1+k}=\frac{\frac{1}{k}}{1+\frac{1}{k}}\leq \ln(1+\frac{1}{k})\leq\frac{1}{k}$

Prove the following: $$\frac{1}{1+k}=\frac{\frac{1}{k}}{1+\frac{1}{k}}\leq \ln(1+\frac{1}{k})\leq\frac{1}{k}$$ I know I can prove it with induction if the values were naturals. However, the "problem" ...
1
vote
1answer
13 views

Log transformations of function domain and inequalities

If I know that for some function $f$, the following is true for $x, y \geq 0$: $f(\log (x^a y^b)) \leq f(\log x)^a f(\log y)^b$ Can I make the claim that $f(x^a y^b) \leq f(x)^a f(y)^b$ If I ...
3
votes
7answers
73 views

Evaluating $\lim_{n\to\infty}{n\left(\ln(n+2)-\ln n\right)}$

I am trying to find$$\lim_{n\to\infty}{n\left(\ln(n+2)-\ln n\right)}$$ But I can't figure out any good way to solve this. Is there a special theorem or method to solve such limits?
0
votes
0answers
21 views

Applying Cauchy-Riemann to $f(z)$

$$\ln|z|+i\text{Arg}(z)$$ the problem states that I have to apply Cauchy Riemann to the problem and determine a conclusion. Below is how far I got, but I'm not sure how to take the derivative of ...
0
votes
0answers
24 views

How to solve inequalities where the $x$ term appears inside the argument of multiple different functions?

We're asked to study the sign of the following function: $$\frac{x(\ln{x}+1)^2 - 2(\ln{x}+1)^2 - \frac{4}{x(\ln{x}+1)}}{(x(\ln{x}-1)^2)^2} \geq0,$$ in which the $x$ variable appears both outside ...
1
vote
2answers
48 views

Calculate Ln$(i^i)$

Calculate Ln$(i^i)$ My attempt: Ln$(z)$=$\ln|z|+i\arg z$ $$z=0+i^i=0+i\cdot i$$ $$|z|=\sqrt{0^2+i^2}=i\\ \arg z=\arctan(i/0)$$ $1.$ how it can be that the modulus equal to $i$? $2.$ how ...
1
vote
1answer
29 views

How to solve for a variable in logarithms

How do I solve this for $y$? $$u= 1 - \exp\left\{-\left(\frac{y-\theta}{\alpha}\right)^\gamma\right\}.$$ If I take the $\log$ I end up with $$\log(1-u) = ...