Question

Logaritimo 0,5=x na base 4

Answer 1

$\textbf{Dados:}\ \boxed{\mathrm{\log_b{a}=x\Longleftrightarrow b^x=a}}\ \ \bigg\|\ \ \boxed{\mathrm{\dfrac{1}{k}=k^{-1}}}\\\\\\ \mathrm{\log_4{0,5}=x\ \to\ \log_4{\dfrac{1}{2}}=x\ \to\ 4^x=\dfrac{1}{2}\ \to}\\\\ \mathrm{\to\ (2^2)^x=2^{-1}\ \to\ 2^{2x}=2^{-1}\ \to\ 2x=-1\ \to\ \boxed{\mathbf{x=-\dfrac{1}{2}}}}$