Question

Simplifique a expressão:

log3 5. log4 81. log25 ∛2 .

CASO NÃO ENTENDER, SEGUE A IMGEM ABAIXO: OBRIGADA

Answer 1

$log_3 5.log_481.log_{25}{\sqrt[3]{2}}=\\\\ =log_3 5.{\frac{log_2 81}{log_2 4}}.{\frac{log_5 \sqrt[3]{2}}{log_5 25}}=\\\\ =log_3 5.{\frac{log_2 3^4}{log_2 4}}.{\frac{log_5 2^{\frac{1}{3}}}{log_5 25}}=\\\\ =log_3 5.{\frac{4.log_2 3}{2}}.{\frac{{\frac{1}{3}}.log_5 2}{2}}=\\\\ =log_3 5.{log_2 3}.{{\frac{1}{3}}.log_5 2}=\\\\ =(\frac{1}{3}).log_3 5.{log_2 3}.{log_5 2}=\\\\ =(\frac{1}{3}).1=\\\\ =\frac{1}{3}\\\\\\  Obs.: Propriedade: \ log_a b . log_b a = 1\\\\ log_a c . log_b a . log_c b= 1$