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: $7$