# Sample quiz on logarithmic functions Main home here.

1. What is the relationship between the functions $f(x)=2^x$ and $g(x)=\log_2(x)$?
A: they are reciprocals of each other
B: they are translations of each other
C: they are inverses of each other
D: they are both rational functions
2. What is the domain of the logarithmic function $y=\log x$?
A: $\{x\in\mathbb{R}|x>0\}$
B: $\{x\in\mathbb{R}|x\neq 0\}$
C: $\{x\in\mathbb{R}|x\geq 0\}$
D: $\{x\in\mathbb{R}|x>1\}$
3. What is the range of the logarithmic function $y=\log x$?
A: $\{y\in\mathbb{R}|y>0\}$
B: $\{y\in\mathbb{R}|y\neq 0\}$
C: $\{y\in\mathbb{R}|y>1\}$
D: $\{y\in\mathbb{R}\}$.
4. Find the equation of the vertical asymptote of the function $y=\log(x+4)$
A: $y=-4$
B: $x=-4$
C: $x=4$
D: $x=0$
5. Find the $x$-intercept of the function $y=\log_{2}(x-2)$
A: $x=3$
B: $x=2$
C: $x=1$
D: $x=0$
6. Rewrite $y=3^x$ in logarithmic form.
A: $y=\log_{3}x$
B: $y=\log_{x}3$
C: $x=\log_{3}y$
D: $x=\log_{y}3$
7. What transformation takes $f(x)=\log x$ to $g(x)=\log(4x)$?
A: a vertical stretch by a factor of $4$
B: a horizontal stretch by a factor of $4$
C: a horizontal compression by a factor of $\frac{1}{4}$
D: a vertical compression by a factor of $\frac{1}{4}$
8. Rewrite the equation $y=\log_{6}(\frac{1}{216})$ in exponential form.
A: $216=6^y$
B: $\frac{1}{216}=y^6$
C: $y\frac{1}{216}=6^y$
D: $\frac{1}{216}=6^y$
9. Find the value of $\log_{3}(729)$
A: $243$
B: $\frac{1}{243}$
C: $\frac{1}{6}$
D: $6$
10. Relative to the parent function $f(x)=\log_{2}(x)$, how many transformations are in $g(x)=-2\log_{2}(-2x-2)-2$?
A: $4$
B: $5$
C: $6$
D: $7$