Question

log de base 4 2raiz2

Answer 1

$\mathrm{\ell og}_{4\,}(2\sqrt{2})=x\;\;\Rightarrow\;\;4^{x}=2\sqrt{2}\\ \\ \\ (2^{2})^{x}=2\cdot \sqrt{2}\\ \\ 2^{2x}=2^{1}\cdot 2^{1/2}\\ \\ 2^{2x}=2^{1+(1/2)}\\ \\ 2^{2x}=2^{3/2}\\ \\ \\ 2x=\dfrac{3}{2}\\ \\ 4x=3\\ \\ x=\dfrac{3}{4}\\ \\ \\ \Rightarrow\;\;\boxed{ \begin{array}{c} \mathrm{\ell og}_{4\,}(2\sqrt{2})=\dfrac{3}{4} \end{array} }$