How do you solve this step by step? Exponential and logarithmic function

Question

Please help on my homework on exponential and logarithmic functions:

Exponential & Logarithmic Function EDIT: Question is on the link

Answer 1

Familiarize yourself with the basic properties of logarithms.

$$ ln\left(\frac{A}{B}\right) = ln(A) - ln(B) $$ $$ ln(A^x) = x\cdot ln(A) $$ The above should help.

Make sure you understand what a logarithm to the base $e$ is if you do not already and the answer should follow immediately.

Answer 2

Ans:B

$x-ln(1+e^x)$

write the $x$ in the expression as $ln (e)^x$ so that the expression becomes $ln (e)^x$$-ln(1+e^x)$ that is $ln\frac{ (e)^x}{1+e^x}$ because

$ln(\frac{C}{D}) = ln(C) - ln(D)$