All Questions
12
questions
0
votes
1
answer
132
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Simplifying the expression $\frac{1}{3} \ln (x+2)^3+\frac{1}{2}\left[\ln x-\ln \left(x^2+3 x+2\right)^2\right]$ [closed]
Express as a single logarithm. Simplify.
$$
\frac{1}{3} \ln (x+2)^3+\frac{1}{2}\left[\ln x-\ln \left(x^2+3 x+2\right)^2\right]
$$
So I am posting the question, how I solved it and then how the TA ...
- 137
4
votes
3
answers
586
views
I don't understand $\ln$ properties when it comes to absolute value.
Let's say we have a function with absolute value like:
$f(x) = \ln\vert x\vert$ where $x$ is any real number except 0
Now, when we get rid of the absolute value, we get this:
$f(x) = \ln(x)$ where $x$ ...
- 433
2
votes
2
answers
303
views
Logarithm power rule does not provide a complete solution. Have the logarithm rules failed me?
I am solving this question:
$log_3(m-7)^2 = 4$
There are two ways to solve it.
The first way (expand the brackets):
$log_3(m^2 -14m + 49) = 4$
$m^2 - 14m + 49 = 3^4$
$m^2 - 14m - 32 = 0$
$m = 16,-2$
...
- 434
2
votes
3
answers
97
views
How can I solve the following inequality?
I have the inequality:
$lg((x^3-x-1)^2) < 2 lg(x^3+x-1)$
And I'm not sure how should I go about solving it. I wrote it like this:
$2lg(x^3-x-1) < 2lg(x^3+x-1)$
$lg(x^3-x-1) < lg(x^3 + x - ...
user592938
0
votes
1
answer
58
views
Can't find the set of solutions
Set of solutions of this inequality :
$$\log_2({ \space x ^2 - 1}) < 1$$
The answer given is :$$ \sqrt3 < x < - 1 \cup 1 < x < \sqrt3 . $$
4
votes
2
answers
268
views
Natural logarithm with absolute value: Can I cancel the absolute value?
I was calculating basic rational integrals and came up with this kind of problem. I have this expression:
$$2\ln|x|$$
I can re-write it down like that:
$$\ln{x^2}$$
and thus cancel the modulus.
...
- 1,392
1
vote
2
answers
97
views
Expanding log problem
I found this site with online problems and answers.
https://courses.lumenlearning.com/waymakercollegealgebra/chapter/expand-and-condense-logarithms/
I've tried several problems and my answer is ...
0
votes
1
answer
65
views
Log power rules - error in thinking
I am trying manipulate an equation with logs, and I am 99% sure that there is something going wrong in my thinking.
I started of with seomthing like this:
$-\log Ae^x$
using log rule $\log AB = \...
- 75
1
vote
2
answers
299
views
Solving $|x-1|^{\log^2(x)-\log(x^2)}=|x-1|^3$
Solve the equation:$$|x-1|^{\log^2(x)-\log(x^2)}=|x-1|^3.$$
There are three solutions of $x$: $10^{-1}$, $10^3$ and $2$. I obtained the first two solutions but I have been unsuccessful in getting $2$ ...
- 587
5
votes
3
answers
2k
views
How to solve this logarithm inequality with absolute value as its base?
How to deal with this ?
$$\log_{|1 - x|} (x+5)>2 $$
the $|1-x|$ is the base of the logarithm.
I tried this below approach but it seems not the complete solution.
\begin{align}
\frac{\log(x+5)}{\...
- 177
2
votes
1
answer
657
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 ...
- 123
0
votes
1
answer
160
views
Find the value of this logarithmic expression involving fifth root of unity.
Let $\alpha$ be the fifth root of unity. We then want to evaluate the
expression $$\log |1 + \alpha + \alpha^2 + \alpha^3 - 1/\alpha |$$
Thanks in anticipation for your help in solving this!
- 103