Verified answer

[tex]\displaystyle \sf 2^{x}=5^{(x+2 )} \\\\ 2^x=5^x\cdot 5^2\\\\ \frac{2^x}{5^x} = 5^2 \\\\\\ \left(\frac{2}{5} \right)^{x} = 5^2 \\\\\\ \ln \left(\frac{2}{5} \right)^{x} = \ln (5^2 ) \\\\\\\ x \cdot \ln\left(\frac{2}{5} \right)= 2\cdot \ln 5 \\\\\\ x = \frac{\displaystyle 2\cdot \ln 5}{\displaystyle \ln \left(\frac{2}{5} \right)} \\\\\\ \large\boxed{\sf \ x = \frac{2\cdot \ln 5}{\ln 2-\ln 5 } \ }\checkmark[/tex]

Resposta:

[tex]\textsf{Leia abaixo}[/tex]

Explicação passo a passo:

[tex]\Large \boxed{\sf 2^x = 5^{x + 2}}[/tex]

[tex]\Large \boxed{\sf 2^x = 5^x\:.\:5^2}[/tex]

[tex]\Large \boxed{\sf \left(\dfrac{2}{5}\right)^x = 25}[/tex]

[tex]\Large \boxed{\sf log\left(\dfrac{2}{5}\right)^x = log\:25}[/tex]

[tex]\Large \boxed{\sf x\:.\:log\left(\dfrac{2}{5}\right) = log\:25}[/tex]

[tex]\Large \boxed{\sf x = log_{(0,4)}\:25}[/tex]