Question

Sabendo que log2=0,3 e log3=0,48, resolva: 15^x=36

Answer 1

Resposta:

Explicação passo a passo:

$log\:2=0,3$

$log\:3=0,48$

    $15^{x} =36$

 $x=log_{\;15} \:36$

$Vamos\:passar\:pra\:base\:10\:ok!$

$log_{\;15} \:36=\frac{log\:36}{log\:15} =\frac{log\:2^{4} }{log\:(3\:.\:5)} =\frac{4\:.\:log\:2}{log\:3\:+\:log\:5}$

$Observacao...$

$log\:10=1$

$log\:5=log\:(\frac{10}{2}) =log\:10-log\:2=1-0,3=0,7$

$Portanto...$

$log_{\;15} \:36=\frac{log\:36}{log\:15} =\frac{log\:2^{4} }{log\:(3\:.\:5)} =\frac{4\:.\:log\:2}{log\:3\:+\:log\:5}=\frac{4\:.\:(0,3)}{0,48\:+\:0,7} =\frac{1,2}{1,18} =1,0169$