Question

Determine o valor de log25 100, sabendo que log10 5 = a

Answer 1

Explicação passo-a-passo:

Lembre-se que $\sf log_{b}~a=\dfrac{1}{log_{a}~b}$

Logo:

$\sf log_{25}~100=\dfrac{1}{log_{100}~25}$

Temos que $\sf log_{b^{m}}~a^n=\dfrac{n}{m}\cdot log_{b}~a$

Assim:

$\sf log_{25}~100=\dfrac{1}{log_{100}~25}$

$\sf log_{25}~100=\dfrac{1}{log_{10^2}~5^2}$

$\sf log_{25}~100=\dfrac{1}{\frac{2}{2}\cdot log_{10}~5}$

$\sf log_{25}~100=\dfrac{1}{1\cdot a}$

$\sf log_{25}~100=\dfrac{1}{a}$