1
vote
3answers
69 views

Solution for $x$ with exponents?

I am trying to solve the following, $$7^{(2x+1)} + (2(3)^x) - 56 = 0$$ Should I put the 56 on the other side and get the log of both sides and is there a better way to solve this.
0
votes
3answers
26 views

How do you solve a equation by converting to logarithm form for the problem$3e^{x-4} +2=83$?

$3e^{x-4} +2=83$ I understand converting logarithms but i dont understand how to convert e into log form and solve. help would be deeply appreciated.
3
votes
0answers
32 views

Exercise concerning logarithms…

I have such a problem: find all the values of real parameter "a", for which the following inequality is true for any "x" that belongs to R. I will show you my solution, and please can you verify ...
0
votes
0answers
20 views

Summation of a function with the variable both in the function amd in the upper limit

E is defined as : E = c1 ( a$\rho$ + b$\rho ^{2}$ ) + c2 $\rho$ ( c + d $\sum_{j=0}^{n} (\log{ \frac{R\rho}{j} } ) $ ) + c3 $\rho ^{2}$ a, b, c, d, c1, c2, c3, R are known constants. $\rho$ is the ...
1
vote
3answers
33 views

A question on Logarithms

Q: Given that $\log_3(x) = a$ solve for $x$, $\log_3(9x) + \log_3(\frac{x^3}{81}) = 3$ \I make progress by writing $\log_3(9x) = 3^{2+a}$ and $\log_3(\frac{x^3}{81}) = 5a - 4$. However, I can't ...
0
votes
1answer
17 views

clarification on logarithm problem

I was wondering if someone could explain what is going on in this problem. I understand that it makes sense that $(x = 0)$ I'm not sure why $(x<0)$ or $(x>0)$ are ruled out. LS and RS mean ...
3
votes
3answers
164 views

Solving ${\sqrt2}^{\,x} = {\sqrt3}^{\,x}$

I am studying logarithms and exponents. I am not sure how to go about solving this problem. I seem too keep going in circles using the rules of log and exp. $$(\sqrt{2})^x = (\sqrt{3})^x$$
0
votes
1answer
42 views

Logarithms with trigonometric inequality

My class is going to have an exam tomorrow, but we can't figure out how to solve such equations. $$\log_{\ \large tg(x)} \sqrt{\sin(x)^2 - 5/12} < 1 $$ We tried to transform $1$ to $\log_{\ ...
0
votes
1answer
16 views

Conversion of bases with logarithms

The question says if $\log_6(2)$ is $a$ and $\log_5(3)$ is $b$, express $\log_5(2)$ in terms of $a$ and $b$. I have tried the change of base formula for $ab$ to no avail, can someone give me a hint ...
0
votes
0answers
54 views

Complex exponentiation

So I've got this question that is a bit difficult to ask, since it uses a term in my language that I can't properly translate into English. For $z\in\mathbb{C}^*$ and $a\in\mathbb{C}$ it would be ...
0
votes
2answers
36 views

Help finding value of x in logarithms?

How to find the value of x in: $$10=8.4\log(0.3x+1)$$ so far I got : $$10=\log(0.3x+1)^{8.4}$$ $$10^{10}=(0.3x+1)^{8.4}$$ What should I do next?
1
vote
1answer
64 views

Derivative of $\operatorname{Log}(\operatorname{Log}(z^2))$

Please help me with this question: (i don't know how to start) Suppose that $f(z)$ = $\operatorname{Log}(\operatorname{Log}(z^2))$. Find $f'(z)$ where it exists, and determine the set of points at ...
0
votes
1answer
28 views

Numerical Analysis - show something about the rate of convergence

We are given an iterative method for finding roots, $x_{n+1}=g(x_n)$, we are given the rate of convergence of this method is $p$, and also that: $$\lim _{n \to \infty} \frac{|e_{n+1}|}{|e_{n}|^p} = ...
2
votes
1answer
155 views

Find the volume of the solid obtained by rotating the region bounded by $y = ln x$, $y = 0$, $x = 2$ about the $x$-axis

I have the problem: Assuming $y = ln(x)$, and $y = 0$, find the volume bound by these two lines and the point $x = 2$ if the area were rotated around the $x$-axis. I ended up with $2\pi\int_1^2 ...
2
votes
1answer
162 views

Logarithms melting my brain

So I've got an inequality: $\ln(2x-5) > \ln(7-2x)$ and I attempt to solve by doing the following: $$\frac{\ln(2x)}{\ln(5)} > \frac{\ln(7)}{\ln(2x)}$$ $$\Rightarrow \ln(2x) \cdot \ln(2x) > ...
1
vote
2answers
57 views

Changing base of a logarithm by taking a square root from base?

From my homework I found $$\log_9{x} = \log_3{\sqrt{x}}$$ and besides that an explanation that to this was done by taking a square root of the base. I fail to grasp this completely. Should I need to ...
1
vote
2answers
24 views

Continuous compounding question

A population of rabbits starts out with $100$ rabbits. The growth rate is $11.7$% per day. Determine the exponential equation. Is it $$\mathbb {P(t)} = 100e^{11.7t}$$ Can you guys give me the ...
1
vote
0answers
22 views

Mapping a deleting ray to a horizontal strip

So, this is my question: D is a domain obtained by deleting the ray $x\leq 0$. And $G(z)$ is a branch of $log(z)$ on $D$. I want to show that G maps D onto a horizontal strip of width $2\pi$. Show ...
0
votes
1answer
115 views

Logarithmic inequalities

Full disclosure: This is a homework problem, but my question is regarding a concept that came about during solving the problem, not the actual solution to the problem. Problem: Rewrite as geometric ...
2
votes
2answers
71 views

Evaluating limit using logarithms.

Evaluate the following limit. $$ \lim_{x\to \infty} (\ln\ x)^{\frac{1}{x}} $$ What i have tried: $$ \ln\left[\lim_{x\to \infty} (\ln\ x)^{\frac{1}{x}}\right] $$ $$ \lim_{x\to \infty} \ln(\ln ...
0
votes
3answers
60 views

Logarithm properties doubt

The problem is $\log (5.64)^4$. According to the properties and laws of exponents, $\log (m^r) = r \log (m)$. But since the exponent is outside of the parenthesis in this problem, does it solves by ...
-1
votes
1answer
31 views

Expressing an algebraic function as Single Logarithm [closed]

Express $$\log x-2 \log x+3 \log(x+1)-\log(x^2-1)$$ as a single logarithm
-1
votes
4answers
109 views

Help me to Prove that log2 3 is irrational. [closed]

seemingly simple homework assignment, help? Was never the best with logarithms, how would I go about proving? Sorry the question read IRrational!
2
votes
1answer
41 views

Simplifying an expression using a logarithm

I have the following expression $$\frac{1}{1+\rho}(1+n)^{(1-\sigma)}*(1+\gamma_{A})^{1-\sigma}<1$$ and have to use logarithms to get the following $$(1-\sigma)(n+\gamma_{A})<\rho$$ Could ...
0
votes
1answer
31 views

Asset Depreciation - Logarithms

How many years would it take for the value of a car purchased at 30 000 to fall to 15 000 if it depreciates by 15% in the first year and 12% every year after that? This is not actually graded ...
4
votes
1answer
85 views

Proof of $e^{\ln(x)\ln(2)}$, which natural logarithm do I bring down?

I'm currently stumped with the proof for the following problem: $$F(x) = 2^{\ln(x)}$$ $$\Rightarrow F(x) = y$$ $$y = 2^{\ln(x)}$$ $$\ln(y) = \ln(2^{\ln(x)})$$ $$\ln(y) = \ln(x)\cdot\ln(2)$$ $$y = ...
0
votes
2answers
39 views

How do I evaluate this log expression?

Evaluate the expression $\log_8{8^{17}}$ I ended up getting $8^x = 8^{17}$. I'm guessing I find x, but that's a huge number, and I feel like I'm doing this wrong.
0
votes
1answer
37 views

How to simply this logarithmic equation?

I have $$f(L) = M^{L-1} / (M+1) ^L $$ and $$ L = \log_M ((K+B)/A)$$ I am suppose to simply this to $$f = C(K+B)^{-b}$$ with $$ b = \dfrac{\ln(M+1) }{ \ln(M)}$$ for the top I have simplified ...
1
vote
1answer
53 views

$p$-adic logarithm

For $q\in\mathbb{C}_p$ such that $|q|_p < 1$ show that there exists a unique logarithm $\log_q:\mathbb{C}_p^{*}\to\mathbb{C}_p$ with (i) $\log_q(q)=0$ (ii) $\forall x\in\mathbb{C}_p$, ...
1
vote
1answer
43 views

Logarithmical equation with addition of powers

I just wonder how to solve the equation: $$ 3^x + 3 \times 9^x = 1200 $$ Mi first idea was to replace $ 9^x $ with $ 3^{2x} $. Then I can mutliply the powers: $$ 3^x + 3^{2x+1}= 1200 $$ But how to ...
2
votes
1answer
156 views

Find derivation (dB/decade) for given amplitude characteristic of low pass filter [Hz, -]

I am trying to find derivation (differential attenuation) for frequency's 600 and 2000 Hz for given amplitude characteristic of low pass filter, which look like this: I assume, that I should ...
3
votes
5answers
174 views

How to prove that $\ln(x)<x$ for $x\to \infty$?

During my calculus homework I need to prove some limits without using L'Hôpital's rule. I have difficulties to show rigorously that $\ln(x)<x$ for big enough x. For example, I need to find the ...
0
votes
1answer
81 views

How to solve the following equation?

I have been given this equation for homework and I don't know how to solve it. $y=\dfrac{\ln\left(\dfrac{x}{m}-sa\right)}{r^2}$
2
votes
1answer
50 views

Show that $\operatorname{ln}(n!)=\Theta(n\operatorname{ln}(n))$

Another question about asymptotic approximations. We are asked to show that $\operatorname{ln}(n!)=\Theta(n\operatorname{ln}(n))$ I'm stuck tho and can use help. What I did is: ...
0
votes
0answers
32 views

check my short simple proof - Functions are of same magnitude. Asymptotic notation.

A simple question with a short solution I thought of, but I would like verification. $f(n)$ is a function that approaches infinity as $n$ approaches infinity. We are asked to show that ...
0
votes
1answer
30 views

Check my short proof - asymptotic approximation, which function is bigger

The goal of this exercise is to show that $\ln(n+1)-\ln(n) = O(\frac{1}{n})$ what I did is: I used the fact that if $f=O(g)$ then $\frac{f}{g}=O(1)$. $\ln(n+1)-\ln(n)=\ln(\frac{n+1}{n}) = \ln(O(1))$ ...
0
votes
3answers
98 views

It's a logarithmic worksheet and O can't solve it.

$\log_ax=p$, $\log_bx=q$ , $\log_{abc}x$=r. What is $\log_cx$?.. It's on my math homework can someone solve it cause I need it.
0
votes
1answer
33 views

Calculating complex logarithm

I have to calculate the following log: a) log(-4) b) log (3i) I don't really know what to do.. a) $ log(-4) = log|-4| + i\cdot arg(-4) + 2ki\pi = log4 + ?? + 2ki\pi$ b) $ log(3i) = log|3i| + i\dot ...
0
votes
0answers
31 views

Proof logarithm equation

I hope I'm in the right corner? I have to show $ ln(\frac{1+x}{1-x}) = 2 \cdot \sum_{n=0}^\infty \frac{x^{2n+1}}{2n+1} $ for |x| < 1. How to do this? I know $ ln(1+x) = \sum_{n=0}^\infty ...
0
votes
3answers
44 views

logarithms and function

If $\log_{2}(f(x)+|\sin x|)=\log_{2} x$ then: A) $f(x)>0$ for each $x \in R$ B) $\lim_{x\to\infty}f(x)= +\infty$ C) the function is strictly increasing D) $f(\pi)=\pi$ So firstly I define ...
0
votes
3answers
65 views

Is there a logarithm function through this three given points?

I've got the task to find a logarithm function which contains the following points: $$\begin{align*} A&(5 \mid 4)\\ B&(3\mid6)\\ C&(2\mid8.5) \end{align*} $$ Now I need to find the ...
-2
votes
1answer
47 views

Precalc - Exponential and Logarithmic Equations

Sales of a product under relatively stable market conditions tend to decline at a constant annual rate in the absence of promotional activities. This sales decline can be expressed by the exponential ...
0
votes
2answers
64 views

logarithms equations, different bases

solve equations: $\log_x 10 +2\log_{10x} 10-3\log_{100x} 10=0$ so I tried to use $\log_a b=\frac{1}{\log_b a}$ but it didn't work for me.
0
votes
2answers
46 views

Use a graph to estimate the time at which the number was increasing most rapidly

For the period from 2000 to 2008, the percentage of households in a certain country with at least one DVD player has been modeled by the function $f(t) = \frac{87.5}{1 + 17.1e^{−0.91t}}$ where the ...
0
votes
1answer
142 views

How should I express one log in terms of others?

Can someone please help me with this logarithmic question? I know it’s easy, but I need to refresh my memory on how to do it. If X=log2 and Y=log3, express log0.6 in terms of X and Y (assume all ...
2
votes
3answers
91 views

Why isn't $2\log(-1)$ real?

In high school we learn that a $a\log[(x)] = \log (x^a)$ From this I would assume $2\log(-1) = \log [(-1)^2]$ However, the first is not real and the second is, according to my calculator and ...
2
votes
2answers
51 views

Changing an exponential function to logarithmic

I have a question stating that $P=75e^{-0.005t}$ and they want to get t by itself. I used the example $y=2^x = x=log_2(y)$ To find that $-0.005t = 75ln(P)$ So $t=\frac{75ln(P)}{-0.005}$ However ...
2
votes
0answers
36 views

How to prove the function is logarithmic with coefficience

I am given a set of properties for an unknown function $f(x)$. In particular, not constantly zero, not negative, additive and continues for any $x$ between 0 and 1. I am asked to show equivalence ...
2
votes
1answer
384 views

How to prove if log is rational/irrational

I'm an english major, now doubling in computer science. The first course I'm taking is Discrete Mathematics for Computer Science, using the MIT 6.042 textbook. Within the first chapter of the book's ...
3
votes
2answers
165 views

Prove that $\log^25 + \log^27 > \log12$.

Prove that $\log^25 + \log^27 > \log12$. What I tried so far: $\log^25 + \log^27 > \log3 + \log4$ $(\log5 + \log7)^2 - 2 \cdot \log5 \cdot\log7 > \log3 + \log4$ But it seems that I'm not ...