Question Type 4: Finding the inverses of logarithmic and exponential functions Exercises

Find the inverse of the function $m(x) = 5 - \ln(2x)$.

Find the inverse of the function $p(x) = 4e^x + 5$.

Find the inverse of the function $g(x) = e^{3x - 4}$.

Find the inverse of the function $h(x) = \ln(x - 1) + 2$.

Find the inverse of the function $k(x) = -\frac{1}{2}\ln(7x - 1) + 4$.

Find the inverse of the function $h(x) = \ln\left(\frac{x + 2}{5}\right)$.

Find the inverse of the function $r(x) = e^{2x} + 3$.

Find the value of $f^{-1}(2)$ for $f(x) = \frac{1}{3} \ln(x)$.

Find the inverse of the function $f(x) = \frac{1}{5}\ln(8x + 2)$.

Find the inverse of the function $q(x) = \log_2(5x + 3) - 1$.

Find the value of $f^{-1}(3)$ for $f(x) = \ln(2x + 7)$.

Find the value of $f^{-1}(3)$ for $f(x) = \frac{1}{4}\ln(3x - 5)$.