Question Type 5: Finding values of the base or the input of a log given one and an exponent Exercises

Find $b$ given $\log_3(b)=4$.

Find $x$ if $\log_{\tfrac{1}{2}}(16)=x$.

Find $x$ if $\log_{\frac{1}{3}}(27)=x$.

Solve for $x$ in $\log_5(x)=2$.

Find $x$ given $\log_4(x)=\tfrac{1}{2}$.

Determine $b$ when $\log_b(81)=4$.

Solve for $a$ in $\log_a\left(\frac{1}{125}\right)=3$.

Solve for $x$ when $\log_{x-1}(9)=2$, given $x>2$.

Determine $a$ when $\log_a(8)=3$.

Find $x$ if $\log_2(x) = -3$.

Find $x$ if $\log_2(x-1)=4$.

Determine $x$ if $\log_x(16)=2$.