Question

calcule o valor de t.
2/3=3^-2t

Answer 1

Olá, boa tarde!

Resposta:

$\boxed{\color{red}{\mathsf{t = -\dfrac{In (\dfrac{2}{3})}{2 \ In (3)}}}}$

Ou

$\boxed{\color{red}{\mathsf{t=0,18453512...}}}$

Explicação passo-a-passo:

$\mathsf{\dfrac{2}{3} = 3^{-2t}}$

$\mathsf{3^{-2t} = \dfrac{2}{3}}$

$\mathsf{In (3^{-2t}) = In \dfrac{2}{3}}$

$\mathsf{-2t \ In (3)= In (\dfrac{2}{3})}$

$\mathsf{t=-\dfrac{In (\dfrac{2}{3})}{2 \ In (3)} \overrightarrow {ou} \ t=0,18453512...}$

=================== Espero ter ajudado ===================

Abraços!