Question

Podem me ajudar nesta questão segue imagem​

Answer 1

Oi!

$\boxed{log(2) = 0,30}$
$\boxed{log(3) = 0,48}$

a)
$4^x = 9 \\ {(2^2)}^{x} = 3^2 \\ {2}^{2x} = 3^2 \\ log({2}^{2x}) = log(3^2) \\ 2x \times log(2) = 2 \times log(3) \\ 2x * 0,30 = 2 \times 0,48 \\ 0,6x = 0,48 \\ x = \frac{0,48}{0,6} \\ \boxed{x = 0,8}$

b)
${12}^{x} = 25 \\ {12}^{x} = 5^2 \\ log({12}^{x}) = log(5^2) \\ x \times log(12) = 2 \times log(5) \\ x \times log(2^2 * 3) = 2 \times log(\frac{10}{2}) \\ x \times (log(2^2) + log(3)) = 2 \times (log(10) - log(2)) \\ x \times (2 \times log(2) + 0,48) = 2 \times (1 - 0,30)\\ x \times (2 \times 0,30 + 0,48 = 2 \times 0,7 \\ x \times (0,60 + 0,48) = 1,4 \\ x \times 1,08 = 1,4 \\ 1,08x = 1,4 \\ x = \frac{1,08}{1,4} \\ x = 0,77$