Question

se log 2 raiz x + log2 1/x= -1, entao log4x é igual a ?

Answer 1

$\text{log}_2\sqrt{x}+\text{log}_2~\dfrac{1}{x}=-1 \\\\ \text{log}_2~x^{\frac{1}{2}}+\text{log}_2~x^{-1}=-1 \\\\ \text{log}_2~(x^{\frac{1}{2}}\cdot x^{-1})=-1 \\\\ \text{log}_2~x^{-\frac{1}{2}}=-1 \\\\ x^{-\frac{1}{2}}=2^{-1} \\\\ (x^{-\frac{1}{2}})^{-2}=(2^{-1})^{-2} \\\\ x=2^2 \\\\ x=4 \\\\ \text{log}_4~x=\text{log}_4~4~\longrightarrow~\boxed{\text{log}_4~x=1}$