Question

sendo logb a=4 e logb c=1 encontre o valor de: logb(√a.c)

Answer 1

$\large\begin{array}{l}\mathsf{\ell og_ba=4~~e~~\ell og_bc=1}\\\\\\\mathsf{\ell og_b( \sqrt{a\cdot c})}\\\\\mathsf{\ell og_b(a\cdot c)^{\dfrac{1}{2}}}\\\\\\\mathsf{\dfrac{1}{2}\ell og_b(a\cdot c)}\\\\\\\mathsf{\dfrac{1}{2}(\ell og_ba~+~\ell og_bc)}\\\\\\\mathsf{\dfrac{1}{2}(4+1)}\\\\\\\mathsf{\dfrac{5}{2}}\\\\\\\fbox{ \mathsf{\ell og_b(a\cdot c)=\dfrac{5}{2}} }\end{array}$