Verified answer

Explicação passo-a-passo:

Acho que vc quis dizer: "Se f(log_{2}(x + 1)) = 256^x

Calcule log_{2}(f(8))"

Sendo assim...

[tex] \\ f( log_{2}(x + 1) ) = f(8) \\ log_{2}(x + 1) = 8 \\ x + 1 = 2 {}^{8} \\ x = 2 {}^{8} - 1 \\ \\ f( log_{2}(x + 1)) = log_{2}(256 {}^{x} ) \\ f( log_{2}(2 {}^{8} - 1+ 1)) = log_{2}(256 {}^{2 {}^{8} - 1 } ) \\ f( log_{2}(2 {}^{8})) = (2 {}^{8} - 1) log_{2}(256) \\ f( 8log_{2}(2)) = (2 {}^{8} - 1) log_{2}(2 {}^{8} ) \\ f(8) = (2 {}^{8} - 1)8 \\ f(8) = 2 {}^{3} (2 {}^{8} - 1) \\ f(8) = 2 {}^{11} - 2 {}^{3} \\ f(8) = 2048 - 8 \\ f(8) = 2040[/tex]