Question

dados log 2 na base a= 0,69 e log 3 na base a = 1,1 calcule log raiz quarta de 12 na base a

Answer 1

$log_{a}2 = 0,69 \\ log_{a}3=1,1 \\ \\ log_{a} \sqrt[4]{12} =log_{a}12^{ \frac{1}{4}}= \frac{1}{4} .log_{a}3.4= \frac{1}{4} .(log_{a}3 + log_{a}4) \\ \\ \frac{1}{4} .(log_{a}3+ log_{a}2^{2})=\frac{1}{4} .(log_{a}3+ 2.log_{a}2) \\ \\ \frac{1}{4} .(1,1 + 2.0,69) = \frac{1}{4} .(1,1 + 1,38) = \frac{1}{4} .(2,48)= 0,62$

Espero ter ajudado.