Question

What is the inverse of f(x)=2^x

Answer 1

Answer:

${f}^{ - 1} (x) = \frac{ln(x)}{ln(2)}$

Step-by-step explanation:

$f(x)=2^x$

$y = {2}^{x}$

$x = {2}^{y}$

${2}^{y} = x$

$ln( {2}^{y} )=ln(x)$

$yln(2)=ln(x)$

$\frac{yln(2)}{ln(2)} = \frac{ln(x)}{ln(2)}$

$y = \frac{ln(x)}{ln(2)}$

${f}^{ - 1} (x) = \frac{ln(x)}{ln(2)}$

Hope it is helpful...