Question Type 5: Finding other values of logarithm Exercises

Given $\log_{b} \tfrac{1}{16} = -4$ (with $b>0$, $b\ne 1$), find $b$.

Given $\log_a 8 = 3$, find $a$ (assume $a>0$ and $a\ne 1$).

Given $\log_{x} \sqrt{2} = \tfrac{1}{6}$ (with $x>0$, $x\ne 1$), find $x$.

Given $\log_a b = \frac{p}{q}$ with $a>0$, $a\neq 1$, express $b$ in terms of $a$, $p$, and $q$ (assume $q\neq 0$).

Given $\log_{\frac{1}{2}} x = -3$, find $x$.

Given $\log_3 b = 4$, find $b$.

Given $\log_{x-1} 16 = 4$ and $x>1$, find $x$.

Given $\log_{\sqrt[3]{x}} \sqrt{y} = 2$ with $x>0$, $x\ne 1$, $y>0$, express $y$ in terms of $x$.

Given $\log_a 27 = \tfrac{3}{2}$, find $a$ (assume $a>0$, $a\ne 1$).

Given $\log_{\sqrt{a}} 16 = 4$ (with $a>0$, $a\ne 1$), find $a$.

Given $\log_{3x} 81 = 2$ with $x>0$, find $x$.

Given $\log_x 81 = 4$ (with $x>0$ and $x\ne 1$), find $x$.