Question

logx 64 = 3
help please

Answer 1

Explicação passo-a-passo:

$\sf{\log_{x} (64) = 3}$

Converta o logaritmo na forma exponencial usando

$\mathbf{\log_{a} (x) = b~\Rightarrow~x = a^b}$

$\sf{64 = x^3}$

$\sf{x^3 = 64}$

$\sf{x = \sqrt[3]{64}}$

M.M.C (64)

$\sf{\begin{array}{r|l} 64&2 \\ 32&2 \\ 16&2 \\ 8&2 \\ 4&2 \\ 2&2 \\ 1\end{array}~~\Rightarrow~~2^3 \cdot 2^3}$

$\sf{x = \sqrt[3]{2^3 \cdot 2^3}}$

$\sf{x = \sqrt[\diagup \!\!\!3]{2^\backslash \!\!\!^3 \cdot 2^\backslash \!\!\!^3 \: }}$

$\sf{x = 2 \cdot 2}$

$\red{\boxed{\sf{x = 4}}}$