1
vote
4answers
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, ...
2
votes
1answer
66 views

What's an intuitive way to compute summation of this series?

What's an intuitive way to compute $$\log(1)+\log (2)+\log (3)+\cdots+\log (n-1)+\log (n)$$ or for $n>a$ $$\log(a)+\log (a+1)+\log (a+2)+\cdots+\log (n-1)+\log (n) $$ I know the answer for ...
1
vote
3answers
39 views

Solve x in logarithm equation

I am trying to solve $x$ for $2log_{10} (x-4) - log_{10}4(x-1) = 0$ I have the key with the answer 10 and have confirmed this is correct using Wolfram Alpha but which steps should I take to reach ...
0
votes
3answers
43 views

Trouble with Logarithmic Differentiation

Hey guys I'm trying to find the derivative of this equation using logarithmic differentiation but I'm having some trouble. Wolfram Alpha is giving me different answers and I'm having difficulty ...
3
votes
2answers
139 views

Exponential function to logarithmic function

i'm stuck on completing this equations. Is this correct? $$z=a e^{-bt}$$ $$\ln(z)=\ln(a)+\ln(e^{-bt})$$ $$\ln(z)=\ln(a)+(1)(-bt)$$ $$\ln(z)=\ln(a)-bt$$
1
vote
1answer
70 views

Why does $\log_{4}32 \neq \log _{4}(4 \cdot 8)$

$$\log_{4}32=2.5$$ If $$\log_{a}(b\cdot c) = \log _{a}b + \log_{a}c \,\,\,; (a>0, b>0,c>0, a\neq 1)$$ Then why does $\log_{4}32$ can't be $\log _{4}(4 \cdot 8)= \log_{4}4+\log_{4}8 = ...
1
vote
3answers
31 views

Solving for the value inside a base 10 logarithm

I have an equation of $\log(d)=(-x-A)/(10n)$ that I need to solve for $d$. How do I "reverse" the logarithm to obtain $d$? I apologize if this is super easy, I just can't even figure out how to Google ...
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
3answers
61 views

Solve logarithmic equation: $2\log_7 (x+2) - \log_7 (3x+10) = 0$ [closed]

Please, can someone check if this is the right answer $$x= -2 \pm \sqrt{3x + 10}$$ Thank you.
2
votes
2answers
86 views

How do I simplify $\log (1/\sqrt{1000})$?

How do I simplify $\log \left(\displaystyle\frac{1}{\sqrt{1000}}\right)$? What I have done so far: 1) Used the difference property of logarithms $$\log ...
7
votes
3answers
192 views

Is $ln(x)$ ever greater than $x$

Is $\forall x \in \mathbb{R}, \ln(x) \lt x$ a true statement? Just wondering for some convergence related thing
0
votes
2answers
37 views

Logorithms on a first level learning

Solve log$_{5x-1}$ $4$ $=$ $1/3$ $(5x-1)^{1/3}$=4 $((5x-1)^{1/3})^3$ = $4^3$ $5x-1=64$ $5x=65$ $13$ I am not sure where to go with this. I learned some things about logs before my class ended ...
1
vote
1answer
31 views

Help with Evaluating a Logarithm

A precalculus text asks us to evaluate $\log_{8}\dfrac{\sqrt{2}\cdot\sqrt[3]{256}}{\sqrt[6]{32}}$ I do the following: $\log_{8}\dfrac{\sqrt{2}\cdot\sqrt[3]{(2^2)^3\cdot 2^2}}{\sqrt[6]{2^3\cdot 2^2}}$ ...
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
45 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
22 views

If $g(x) = \text{arctanh}\ (\log x)$, find $g'(x)$.

If $g(x) = \text{arctanh}\ (\log x)$, find $g'(x)$. I tried to separate the terms first and I got $\dfrac12 (\log(1+\log x) - \log(1-\log x))$. The answer is $\dfrac1{x(1-\log x)^2}$.
0
votes
2answers
35 views

Given that $\log_2(x)=p$ and $\log_4(y)=q$, how do I evaluate $\log_x(4y)$?

Given that $\log_2(x)=p$ and $\log_4(y)=q$, how do I evaluate $\log_x(4y)$? There were some other questions like this and I applied this formula to them $\log_a(xy) = \log_a(x)+\log_a(y)$. However, in ...
3
votes
4answers
73 views

Solve for $x$ in $2\log(x+11)=(\frac{1}{2})^x$

Solve for $x$. $$2\log(x+11)=(1/2)^x$$ My attempt: $$\log(x+11)=\dfrac{1}{(2^x)(2)}$$ $$10^{1/(2^x)(2)}= x+11$$ $$x=10^{1/(2^x)(2)}-11$$ I'm not sure what to do next, because i have one $x$ in ...
1
vote
3answers
55 views

Why $\ln 2=\ln 1.075^t\implies \ln 2=t\ln 1.075$

Why $$\ln 2=\ln 1.075^t\implies \ln 2=t\ln 1.075$$
2
votes
1answer
28 views

Exponential continuous growth $\ln a$ vs. $r$? Huh?

So, given a simple population continuous growth problem, it seems that the entirety of the internet uses $P=P_0e^{rt}$ where $P$ is the population over time, $P_0$ is the initial population, $r$ is ...
2
votes
2answers
47 views

Expressing $\ln \sqrt[3]{54}$ in terms of $\ln 2$ and/or $\ln 3$

Express $\ln \sqrt[3]{54}$ in terms of $\ln 2$ and/or $\ln 3$ I know that $\sqrt[3]{54}=54^{1/3}$ but otherwise I don't know how to address these types of problems. How do I solve this, and is ...
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 ...
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: $M=log(\frac{1900000}{1000})$ $10^M = \frac{1900000}{1000}$ ...
6
votes
3answers
96 views

What is the value of $\ln \left(e^{2 \pi i}\right)$

I know that $$e^{2 \pi i} = 1$$ so by taking the natural logarithm on both sides $$\ln \left(e^{2 \pi i}\right)=\ln (1)=0$$ however, why isn't this $2 \pi i$ as expected? Is it beacuse logarithms ...
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
1answer
45 views

Solve $\log_2 (1+\frac{1}{x-1})<1$

I don't get how my teacher got two different equations out of the one. One is $> 0$ and the other one is $<2$. Be detailed please.
0
votes
1answer
39 views

Extraneous solutions where they come from?

I was doing some homework on logarithmic equations, and when I check my solutions on wolfram alpha I get that some aren't. So I'm interested in where do those extraneous equations come from?
1
vote
1answer
12 views

Insert Means in an Arithmetic Sequence (that contains logarithms)

So the question is: You have an Arithmetic Sequence. Log 2 and Log 1024 are two terms in the sequence Find 8 arithmetic means between them.
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
4answers
62 views

Solving a logarithmic system of equations

I am working on a test study guide and I can't seem to get the correct answer for this system of equations: \begin{align*} \ln(x) &= 3\ln(y) \\ \ 3^x &= 27^y \end{align*} I'm not ...
0
votes
3answers
28 views

Logarithm Equations: Solving for variable

This is similar to the last question I asked, but I am just unsure about how to work this problem. The equation is $2\ln(x) + 3 = 0$ Please show the steps.
1
vote
3answers
33 views

Logarithmic equations: Solving for the Variable

The equation is $(3/2)\ln x= -2$. I am not sure how to work this one. If anyone could show all the steps that would be a great help. I tried working it out and got down to $x^{3/2}=e^{-2}$ that is ...
2
votes
4answers
42 views

Logarithmic Equations and solving for the variable

The equation is $\ln{x}+\ln{(x-1)}=\ln{2}$ . I have worked it all the way through, and after factoring the $x^2-1x-2$ I got $x=2$, $x=-1$, but my question is: Can we have both solutions or couldn't we ...
0
votes
1answer
38 views

Logarithmic Equations: Solving for the unknown variable

What is $y$ in $$3^{2y}\cdot3^{\log_{3}(1/3)}=9$$ I apologize if this is confusing, i wasn't sure how to type this equation in here to ask it. If you can please show the steps it would help me ...
0
votes
0answers
26 views

Is this basic proof complete?

I have a problem with proving that the limit as x goes to infinity for lnx/x is 0. Take the most basic approach: Note that the derivative of lnx is 1/x whereas x has a derivative of 1. Hence, lnx is ...
0
votes
1answer
25 views

Change base log formula?

Im trying to change the base log from ln to log with the following formula. y = a * ln⁡(x+c) + b The ln equation is: ...
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.
0
votes
1answer
35 views

Prove this logarithm equation

I keep getting the wrong answer. Can someone please correct my working out a^x=b^(1-x) In(a)^x=In(b)^(1-x) xIn(a)=(1-x)In(b) xIn(a)=In(e)-xIn(b) xIn(a)+xIn(b)=In(e) x[In(a)+In(b)]=Ine ...
0
votes
1answer
45 views

Inverse Function of Logarithm

The answer is A but I don't understand why! $ -2 \log_e (x^2) $ can be re-written as $ -4 \log_e(x) $ right? but why do these two graphs look different? the graph $-2 \log_e (x^2) $ is one to ...
0
votes
1answer
17 views

Maximum value of constant in logarithm problem

The first thing I did was: make: (x-1)^2 - k > 0 (x-1)^2 > k don't know what to do after this point... the maximum value of k is 9 i dont really understand what the maximum value of k is? ...
1
vote
0answers
32 views

Interchanging from exponential form to log form

Shouldn't the answer be x = loge(everything else in the bracket) why is the loge function divided by "k" ???
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 ...
1
vote
1answer
24 views

Sketching Logs with Quadratic Terms

$\log(x^2+1) = y$ asymptote at $x^2+1 > 0$ and so there is no asymptote $x$ and $y$ intercept at $(0,0)$ How do you know that the function goes both directions, and has a dip in the middle? ...
0
votes
2answers
61 views

2 questions regarding logarithms

Sorry the tag is probably wrong but I honestly don't know what logarithm should be under. There are 2 similar questions on $\log$ that I'm unable to solve. Given that $\log_a xy^2 = p$ and ...
11
votes
1answer
513 views

Interesting negative decimal number notation

I was studying logarithms, and had to solve the problem: If $\log 8 = 0.90$, find $\log 0.125$. I found out the answer to be $-0.90$. That was easy. But my text book has given the answer as: ...
1
vote
3answers
40 views

Logarithmic equation help

$\log _5\left(x+3\right)+\log _5\left(3x-5\right)=\log _{25}\left(9x^2\right)$ I have the answer: $\left\{\frac{\sqrt{181}-1}{6}\right\}$ (only answer that falls in the domain) i understand how to ...
0
votes
4answers
157 views

How can $\frac12 \log(x) = \log(\sqrt{x})$?

How can $\frac{\log (x)}{2}= \log \left(\sqrt{x}\right) \\$? How would I come to this conclusion?
1
vote
3answers
107 views

$3^{2x} - 34(15^{x-1}) + 5^{2x} = 0$

I've never seen anything like this. Do somebody have a way to solve it? I've tried the basci exponential functions techniques but it does not work. Even substitution does not work... I'm really ...