Question

equação exponencial
${9}^{ \times - 2} = \sqrt{2}$
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Answer 1

Olá! então...

9^(x-2)=√2

9^2(x-2)=2

9^(2x-4)= 2

3^(4x-8)= 2

propriedade logarítima

log 3 (2)= 4x-8

0,6309= 4x-8

4x=8,6309

x= 2,1577324383...

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{9^{\:x - 2} = \sqrt{2}}$

$\mathsf{(3^2)^{\:x - 2} = \sqrt{2}}$

$\mathsf{3^{\:2x - 4} = 2^{\frac{1}{2}}}$

$\mathsf{log\:3^{\:2x - 4} = log\:2^{\frac{1}{2}}}$

$\mathsf{(2x - 4)\:.\:log\:3 = \dfrac{1}{2}\:.\:log\:2}$

$\mathsf{2x - 4 = \dfrac{1}{2}\:.\:\left(\dfrac{log\:2}{log\:3}\right)}$

$\mathsf{4x - 8 = \left(\dfrac{log\:2}{log\:3}\right)}$

$\mathsf{4x = \left(\dfrac{log\:2}{log\:3}\right) + 8}$

$\boxed{\boxed{\mathsf{x = \dfrac{log_3\:2 + 8}{4}}}}$