Question

Sabendo que log 2 = a. log 3 =b, escreva log5 60 em função de a e b.

Answer 1

Olá Amanda :)

vamos usar as propriedades:

$logxy~\to~logx*y~\to~logx+logy\\\\ log( \frac{x}{y})~\to~logx-logy\\\\ log_yx~\to~\frac{logx}{logy}\\\\ log_xx=1$

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$log_{5}60= \frac{log60}{log5}\\\\ log_560= \frac{log2*3*10}{log \frac{10}{2} }\\\\ log_560= \frac{log2+log3+log10}{log10-log2}\\\\ log_560= \frac{a+b+1}{1-a}$


Espero ter ajudado e tenha ótimos estudos =))