Question

Calcule o logaritmo:

log $\frac{5}{3} \frac{9}{125}$

Answer 1

$log_{\frac{5}{3}}\frac{9}{125}=x\\ \\ \left(\frac{5}{3}\right)^x=\frac{9}{125}\\ \\ \left(\frac{5}{3}\right)^x=\left(\frac{3}{5}\right)^2 \\ \\ \left(\frac{5}{3}\right)^x=\left(\frac{5}{3}\right)^{-2} \\ \\ \boxed{x=-2}$

Answer 2

Oie, Td Bom?!

$= log_{ \frac{5}{3} }( \frac{9}{125} )$

• Reescreva a expressão utilizando a mudança na fórmula da base,$log_{a}(x) = \frac{ log_{10}(x) }{ log_{10}(a) }$ .

$= \frac{ log_{10}( \frac{9}{125} ) }{ log_{10}( \frac{5}{3} ) }$

$≈ \frac{ - 1,14267}{0,221849}$

$≈ - 5,1507$

Att. Makaveli1996