Question

Propriedade de logaritmo.

Sabendo que:

$\boxed{Log _{3} 2= x}$

Calcule:

$9 ^{2x} +81 ^{ \frac{x}{2} }$

Answer 1

$\log_{3}2=x$  ⇒  $3^{x} =2$

$9 ^{2x} +81 ^{ \frac{x}{2} } =$

$( 3^{2} )^{2x} +( 3^{4} )^{ \frac{x}{2} } =$

$3^{2.2x} +3^{ 4.\frac{x}{2} } =$

$3^{4x} +3^{ 2x } =$

$(3^{x} )^{4} +(3^{x} )^{ 2 } =$

$(2 )^{4} +(2 )^{ 2 } =$

$16 +4 =$

$20$

Answer 2

$9^{2x}$  + $81^{x/2}$ =

$3^{2(2x) }$ + $3^{4 (x/2) }$ =

$3^{4x}$ + $3^{2x}$ =

$3^{x(4)}$ +  $3^{x(2)}$ =

$2^{4}$ + 2² =

16 + 4 = 20