Question

log 7 base 7 + log 25 base 5 + log 2√2 base 2 + log 1/3 base 3 - log 1000 base 10 + log 0,01 + 9 elevado log 8 base 9 + log 1 base 4
alguém??

Answer 1

Resposta:

Explicação passo-a-passo:

$log_77+log_525+log_2(2\sqrt{2})+log_3(\frac{1}{3})-log_{10}1000+log_{10}0,01+9^{log_98}+log_41\\\\\\log_77=1\\\\log_525=2\\\\log_2(2\sqrt{2})=log_22+log_22^{\frac{1}{2}}=1+\frac{1}{2}=\frac{3}{2}\\\\log_3(\frac{1}{3})=log_33^{-1}=-1\\\\log_{10}1000=3\\\\log_{10}0,01=log_{10}10^{-2}=-2\\\\9^{log_98}=8\\\\log_41=0\\\\Somando\\\\log_77+log_525+log_2(2\sqrt{2})+log_3(\frac{1}{3})-log_{10}1000+log_{10}0,01+9^{log_98}+log_41=$

$=1+2+\frac{3}{2}-1-3-2+8+0=3+\frac{3}{2}-6+8=5+\frac{3}{2}=\frac{10+3}{2}=\frac{13}{2}$