1
vote
3answers
1k views

What's wrong with my aproach to solving this equation with multiple logarithms?

A question I was faced with asked "For which $x$ is $\log_{10}(x)^{\log_{10}(\log_{10}(x))}= 10,000$?" My instincts tell me I can say $$\log_{10}(x)=10$$ and $$\log_{10}(\log_{10}(x))=4$$ However, ...
4
votes
5answers
379 views

Am I allowed to apply L'Hospital's Rule inside of the natural logarithm function?

I have the following limit: $$\lim_{x\rightarrow \infty} \ln\left(\frac{2x^2+1}{x^2+1}\right)$$ If I was finding the limit of only the terms inside the natural log function, I would have the ...
0
votes
0answers
41 views

solving the logaritham [duplicate]

I was trying to solve: $\log_2 x \cdot \log_{0.25} x \cdot \log_{0.125} x \cdot \log_{16} x > \frac {2}3$ heres my attempt at it; using logaritham laws and a little algebra we get from $\log_2 x ...
-1
votes
2answers
122 views

How to show $\log_2 x \cdot \log_{0.25} x \cdot \log_{0.125} x \cdot \log_{16} x > \frac {2}3$?

I was trying to solve $\log_2 x \cdot \log_{0.25} x \cdot \log_{0.125} x \cdot \log_{16} x > \frac {2}3$ and I keep getting a partial answer of $x>4$ though answer key suggests a more expanded ...
2
votes
2answers
45 views

solving equations with powers

Im trying to solve the equation $$3\cdot2^{-2/x} + 2\cdot9 ^{-1/x} = 5\cdot6^{-1/x }$$ So far I tried applying logaritmas but it didnt prove helpful...are there any other ways?
0
votes
2answers
49 views

Proof the expession $\log_{12}{18}*log_{24}{54} + 5(\log_{12}{18}-log_{24}{54})=1$

I am trying to proof the following expression (without a calculator of course). $\log_{12}{18}*\log_{24}{54} + 5(\log_{12}{18}-\log_{24}{54})=1$ I know this isn't a difficult task but it's just ...
0
votes
2answers
41 views

Help me solve this…

Assuming $a=\log 2$ and $b=\log 3$ (log is the base 10 logarithm). I have to find $\log_5 288$. How can I do this? Edit: I've tried transforming $\log2$ to $\frac{\log_5 2}{\log_5 10}$ and same for ...
0
votes
2answers
49 views

Help me to solve math homework on logarithmic

How to solve this math home work? Please help.. What is the value of $\log \left(\dfrac{i\pi}{2}\right)$ ? I got to know the answer is "$\dfrac{i\pi}{2}$", but don't know how to solve it. Please ...
0
votes
1answer
27 views

Mathematics - geometric progression question

If $a$, $b$ and $c$ are in geometric progression, then what are $\log_ax$, $\log_bx$ and $\log_cx$ in? What I did: I substituted values for $x, a, b$ and $c$ and tried to solve it further. What I ...
2
votes
1answer
57 views

What does this log notation mean?

Can someone please explain what $^2\log x$ means? Is it the same as saying $\log x^2$ or is it something completely different? Here is an image of it as an example:
5
votes
3answers
59 views

Limit of logarithmic function using l'Hospital

How can I find the following limit: $$\lim_{x\rightarrow \infty}\frac{\ln(1+\alpha x)}{\ln(\ln(1+\text{e}^{\beta x}))}$$ where $\alpha, \ \beta \in \mathbb{R}^+$. My first guess was to use ...
0
votes
1answer
21 views

How to clear variable $v$ from logarithmic equation

I have the following: $6.4 = -\log\dfrac{5-v*0.1}{50+v}$ I would like to know how to solve the equation in order to get $v$'s value. Thank you very much.
2
votes
1answer
76 views

-ln(0.1) equalling to ln(10)?

I am having quite a headache wrapping my head around this solution. I do not understand the first line where they get lambda = ln(10) from statement to the left. Somebody please explain this to me. ...
0
votes
4answers
42 views

How do you solve this using only given values, logarithm rules and no calculator?

Given that $\log12=1.0792$ and $\log4=0.6021$, solve $\log8$ without a calculator. I am familiar with the following three rules: Product rule: $\log(a\cdot b)=\log a+\log b$ Quotient rule: ...
1
vote
1answer
28 views

Domain of definition of the function

I was going through some questions of Relations and Functions and now I am stuck to one. Question says Question: Domain of definition of the function $$f(x)=\frac{9}{9-x^2}+\log_{10}(x^3-x)$$ ...
0
votes
1answer
31 views

Sketching the graph of $y =\ln(4-x)$

$y = \ln(4 - x) $ This graph has two operations applied to the $\ln x$ graph - a reflection and a translation. If you reflect the graph in the $y$-axis first, and then shift the graph 4 units to ...
2
votes
1answer
67 views

$\iiint \frac{1}{x^2+y^2+(z-2)^2}dA$ where $A=\{x^2+y^2+z^2 \leq 1\}$ check my answer!

I would like someone to review my solution please, the original question is to calculate $\iiint \frac{1}{x^2+y^2+(z-2)^2}dA$ where $A=\{x^2+y^2+z^2 \leq 1\}$ What I did: First I changed variables ...
0
votes
1answer
28 views

Asymptotic behaviour of a couple of special functions (features exponentials and logarithms)

I'm dealing with a couple of functions: $n \log n$, $( \log \log n)^{ \log n}$, $( \log n)^{ \log \log n}$, $n e^{\sqrt{n}}$, $( \log n)^{ \log n}$, $n 2^{ \log \log n}$, $n^{1+1/( \log \log ...
1
vote
1answer
54 views

Why does this equation work?

let $ P(x) := \sum_{p \leq x} Log [p]$, then we have $P(2^{k+1}) = \sum_{i=0}^k ( P(2^{i+1}) - P(2^i)) < 2 \cdot Log[2] \cdot (1 + 2 + 4 +... + 2^k) \leq 4 \cdot Log[2] \cdot 2^k$. Why does ...
2
votes
2answers
30 views

Maximum likelihood estimate - help with calculating logs!

I'm doing a practice question finding the maximum likelihood estimate, but I'm having a bit of trouble with the actual 'pure' maths bit of it (the differentiation) I don't understand how you go from ...
1
vote
5answers
109 views

solve the equation using logarithms (I think this is easy level)

Solve the equation for $x$ by using base 10 logarithms. $$16\cdot4^{2.5x}=9$$ EDIT: I made a typo (somehow... I was very far off!!) The correct equation is this: $$16\cdot4^{2.5x}=70$$ Can it be ...
3
votes
3answers
133 views

Logarithm base transformation

I am trying to solve a problem which, I think, revolves around base transformation of logarithms. It goes like this: $\log_5\,{\log_6\,{\frac{6x-1}{x+1}}} < ...
1
vote
2answers
29 views

Function application (word problem)

The problem: My work so far: $3=log(\frac{A}{A_0})$--->$10^3=\frac{A}{A_0}$ $\frac{A}{A_0}=1000$ (Am I done there?) Plugging it in: $M=log(\frac{1900000}{1000})$ $10^M = \frac{1900000}{1000}$ ...
0
votes
1answer
59 views

Finding time constants of a circuit?

So this is a homework question and I am having trouble figuring out what they are asking. 'The potential difference (voltage) across the capacitor at time t > 0 is given by $V_C(t) = q(t)/C$. The ...
3
votes
2answers
54 views

How to solve if I have ln on both sides of equation?

I thought this would be a common problem but googling hasn't helped. If I have $\ln(ex)=\ln(y) $ what the next step to solve for $y$?
0
votes
1answer
42 views

Homework help to rearrange formula

Given the equation $${V_m} = u(\ln {m_0} - \ln {m_8}) - g{t_f}$$ I need to solve for ${m_0}$ Here is what I have but it looks messy and I feel like there is sometihng wrong or a better way 1st ...
1
vote
3answers
77 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
41 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
38 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
25 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
166 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
44 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
17 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
63 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
42 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
66 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
35 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
358 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
171 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
113 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
25 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
23 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
176 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
79 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
62 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
4answers
138 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
45 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
40 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 ...