Answer:
[tex] {f}^{ - 1} (x) = \frac{ln(x)}{ln(2)} [/tex]
Step-by-step explanation:
[tex] f(x)=2^x[/tex]
[tex]y = {2}^{x} [/tex]
[tex]x = {2}^{y} [/tex]
[tex] {2}^{y} = x[/tex]
[tex]ln( {2}^{y} )=ln(x)[/tex]
[tex]yln(2)=ln(x)[/tex]
[tex] \frac{yln(2)}{ln(2)} = \frac{ln(x)}{ln(2)} [/tex]
[tex]y = \frac{ln(x)}{ln(2)} [/tex]
[tex] {f}^{ - 1} (x) = \frac{ln(x)}{ln(2)} [/tex]
Hope it is helpful...
