1
vote
2answers
14 views

Which conditions imply $\sup_n |\ln x_n| < \infty$?

I want to find conditions which imply that $\sup_n|\ln x_n| < \infty$. Intuitively I think that $\inf_n x_n > 0$ and $\sup_n x_n < \infty$ should be enough, but I don't know how to write it ...
0
votes
2answers
43 views

Equation with logarithms and absolute value

I have this equation: $$ \ln\frac{2-|y-1|}{1-|y|} = \ln x $$ which becomes $$ \ln(2-|y-1|)-\ln(1-|y|) = \ln x. $$ Can the first term in LHS be written as ...
2
votes
3answers
37 views

How to solve $\lim _{k\rightarrow 1}\dfrac {1+\ln k}{\left| \ln \left( \ln k\right) \right| }$

How to solve $\lim _{k\rightarrow 1}\dfrac {1+\ln k}{\left| \ln \left( \ln k\right) \right| }$ I stucked at the denominator.
0
votes
1answer
101 views

Steps to Graph Exponential Equations & Absolute Value

how to sketch: $-e^{|-x-1|} + 2$ Can someone clarify: $|f(x)|:$ we draw $f(x)$ and then reflect the ($-y$ parts) in the $x$-axis $f|(x)|:$ we draw $f(x)$ and then reflect the ($-x$ parts) in the ...
1
vote
1answer
200 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 ...
0
votes
2answers
47 views

Absolute values in logarithms in a solution of differential equation

How have the moduli signs disappeared in the following step: $$\frac1{k}\left(\ln|g+kv| - \ln|g+ku|\right) = -t$$ Therefore $$ \ln\left(\frac{g+kv}{g+ku}\right) = -kt$$ $g$, $k$ and $u$ are ...
0
votes
1answer
110 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!
3
votes
0answers
88 views

Phrase and symbol for “geometric absolute value”$ e^{|\ln(x)|}?$

I'm calculate the median fractional difference between two vectors (to characterise the error in a quantity with a high dynamic range). If $a/b = 0.1$, the fractional difference is $10$, and if $a/b ...
1
vote
2answers
635 views

Log laws and modulus

If you have the log of a modulus, (like after integration), how do the log laws work? So if you have $a\ln\left|2x-3\right|$ does it become: $\ln\left|(2x-3)^a\right|$ or $\ln(\left|2x-3\right|)^a$, ...
1
vote
2answers
103 views

Simplify $\ln(|x-x^2|) - \ln(|x-1|)$

As the topic says, I need to simplify: $$\ln |x-x^2| - \ln |x-1| $$ I don't know how to approach the problem at all. I'm not asking for the answer, but something to maybe get me going.