Question

sabendo que,
$5 {}^{x + 2} = 100$
calcule
$5 {}^{2x}$

​

Answer 1

Explicação passo-a-passo:

${5}^{x + 2} = 100 \\ log_{5}( {5}^{x - 2} ) = log_{5}(100) \\ x - 2 = log_{5}( {10}^{2} ) \\ x - 2 = 2 log_{5}( {10} ) \\ x = 2 log_{5}(5 \times 2) - 2 \\ x = 2( log_{5}(5) + log_{5}(2) ) - 2 \\ x = 2(1 + log_{5}(2) ) - 2 \\ x = 2 + 2 log_{5}(2) - 2 \\ x = 2 log_{5}(2)$

${5}^{2 x} \\ {5}^{2 \times 2 log_{5}(2) } \\ {5}^{4 log_{5}(2) } \\ {5}^{ log_{5}( {2}^{4} ) } \\ {2}^{4} = 16$

Espero ter ajudado