Question

Calcule o valor da soma S :
a) log 0,001 + log 2^8 - log 3^1
b) log 1/2^1/64 + log √3^81 + log 2√8

Answer 1

E ae mano,

suponho que seja assim que quis escrever:

$S=log0,001+log_28-log_31\\ S=log_{10}0,001+log_22^3-log_33^0~~~~.\\\\ S=log_{10} \dfrac{1}{1.000}+log_22^3-log_33^0\\\\ S=log_{10}10^{-3}+log_22^3-log_33^0\\ S=-3\cdot(log_{10}10)+3\cdot log_22-0\cdot log_33\\ S=-3\cdot1+3\cdot1-0\cdot1\\ S=-3+3-0\\\\ \Large\boxed{\boxed{S=0}}|\\-$

>>>>>>>>>>>>>>>>>>

$S= log_{\tfrac{1}{2}} \dfrac{1}{64}+log_{ \sqrt{3}}81+log_2 \sqrt{8}\\\\ S=-log_22^{-4}+log_{ \sqrt{3}}3^4+log_2 \sqrt{2^3}\\\\ S=-4\cdot(-log_22)+4\cdot log_ {\sqrt{3}}3+log_22^{ \tfrac{3}{2}}\\\\ S=4\cdot log_22+4\cdot log_{3^{ \tfrac{1}{2}}}3+ \dfrac{3}{2}\cdot log_22\\\\ S=4\cdot log_22+4\cdot2\cdot log_33+ \dfrac{3}{2}\cdot log_22\\\\ S=4\cdot1+8\cdot1+ \dfrac{3}{2}\cdot1\\\\ S=4+8+ \dfrac{3}{2}\\\\ \Large\boxed{\boxed{S= \dfrac{27}{2}}}|\\-$

Tenha ótimos estudos mano ;D