Respuesta :

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...