Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Equivalent Quantities: Exponentials and Logarithms, Exercise 41: Chapter review

Write down the equation of the asymptote of $g\left(x\right)=-2+5\log x$.

Describe a series of transformations which map the graph of $f\left(x\right)=\log x$ onto the graph of $g\left(x\right)=-2+5\log x$.

Sketch $f\left(x\right)=\ln x\text{ and }g\left(x\right)=\ln (2-x)$ and the asymptote of $g\left(x\right)$ on same axes for $-4\le x\le 6$.

We have $f\left(x\right)=\ln x\text{ and }g\left(x\right)=\ln (2-x)$. Write down equation of the asymptote of $g(x)$.

For $f\left(x\right)=\ln x\text{ and }g\left(x\right)=\ln (2-x)$, describe a transformation which maps the graph of $f\left(x\right)$ onto the graph of $g\left(x\right)$

For $f\left(x\right)=\ln x\text{ and }g\left(x\right)=\ln (2-x)$, use your sketch to solve the equation to solve $f\left(x\right)=g\left(x\right)$.

The graph of $f\left(x\right)=2^x$ is reflected in both the $x$  and $y$-axes, and then translated $2$ units down to become $g\left(x\right)$. Find the equation of the function $g\left(x\right)$.

$f\left(x\right)=\ln x$ is translated $5$ units to the left and then vertically stretched by a scale factor of $3$ to become $g\left(x\right)$. Find the equation of the function $g\left(x\right)$.