1
vote
3answers
29 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
40 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 ...
-2
votes
2answers
111 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
82 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
182 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
35 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
30 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
39 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
27 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
45 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
28 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
95 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
44 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
35 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
59 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
40 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
37 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
22 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
33 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
44 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
60 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
106 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 ...
1
vote
2answers
51 views

Find $n$ satisfying the equation $[\log_21]+[\log_22]+[\log_23]+\dots[\log_2n]=1538 $

If $[\cdot]$ denotes greatest integer function, then what is the value of natural number $n$ satisfying the equation $$[\log_21]+[\log_22]+[\log_23]+\dots[\log_2n]=1538 ?$$ My try: Note that ...
1
vote
3answers
39 views

How to move from powers to simple logarithms?

I'm following a book that briefly moves from $$16000 \times 2^{\displaystyle \left (-\frac{x}{24} \right )} = 1600$$ to $$x = \frac{24 (\log(2) + \log(5))}{\log(2)}$$ adding the comments that ...
1
vote
2answers
55 views

Solving equations with logarithms

I'm having trouble with solving equations that has logarithms in them. For example: $$x^{\log(x)} = \frac{100}{x}$$ How can I solve this? I have reed about how to do it but when I try to do the same ...
0
votes
5answers
44 views

Express $\log_{3}5$ in terms of $p$ and $q$.

If $p=\lg5$ and $q=\log_{3}2$, express $\log_{3}5$ in terms of $p$ and $q$. Um really confused! How do I solve this?
1
vote
2answers
38 views

If $p=\lg 5$, express the following in terms of $p$.

If $p=\lg 5$, express the following in terms of $p$. Express $\log_{5}2$ in terms of $p$. =$\log_{5}2$ =$\frac{\log_{10}2}{\log_{10}5}$ =$\frac{\log_{10}2}{p}$ Then how to simplify it? My book's ...
1
vote
1answer
26 views

Evaluate $\log_{5}19^2 / (\log_{3}15)$

Evaluate $(\log_{5}19^2)/(\log_{3}15)$ I did this, but I get $1.484$, whereas it's $1.038$ in my book. I used the method: $\log_{a}b = \frac{\log_{c}b}{\log_{c}a}$