Question

como calcular logaritmo com base 5 sobre 2 e logaritmando igual a 125 sobre 8 ?

Answer 1

$\mathrm{\ell og_{\frac{5}{2}}\,}\dfrac{125}{8}=x\\ \\ \left(\dfrac{5}{2} \right )^{x}=\dfrac{125}{8}\\ \\ \left(\dfrac{5}{2} \right )^{x}=\dfrac{5^{3}}{2^{3}}\\ \\ \left(\dfrac{5}{2} \right )^{x}=\left(\dfrac{5}{2} \right )^{3}\\ \\ \\ x=3\;\;\Rightarrow\;\; \boxed{ \begin{array}{c} \mathrm{\ell og_{\frac{5}{2}}\,}\dfrac{125}{8}=3 \end{array} }$