Question

Qual o valor de?
B) log (base3) 72 - log( base3) - log (base3) 2?
C) 1/3.log (base15) 8+2.log (base15) 2+ log (base15) 5-log (base15) 9000?
OBS* preciso de todos os calculos!!!

Answer 1

Vamos utilizar as propriedades:

$log(a.b)=log\,a+log\,b\\\\log\,a^c=c.log\,a$

B)

$log_{_3}72-log_{_3}12-log_{_3}2\\\\log_{_3}72+log_{_3}12^{-1}+log_{_3}2^{-1}\\\\log_{_3}72+log_{_3}\frac{1}{12}+log_{_3}\frac{1}{2}\\\\log_{_3}(72.\frac{1}{12}.\frac{1}{2})\\\\log_{_3}\frac{72}{24}\\\\log_{_3}3\\\\1$

C)

$\frac{1}{3}log_{_{15}}8+2.log_{_{15}}2+log_{_{15}}5-log_{_{15}}9000=x\\\\log_{_{15}}8^\frac{1}{3}+log_{_{15}}2^2+log_{_{15}}5+log_{_{15}}9000^{-1}=x\\\\log_{_{15}}\sqrt[3]{8}+log_{_{15}}4+log_{_{15}}5+log_{_{15}}\frac{1}{9000}=x\\\\log_{_{15}}2+log_{_{15}}4+log_{_{15}}5+log_{_{15}}\frac{1}{9000}=x\\\\log_{_{15}}(2\;.\;4\;.\;5\;.\;\frac{1}{9000})=x\\\\log_{_{15}}(\frac{1}{225})=x\\\\\frac{1}{225}=15^x\\\\\frac{1}{15^2}=15^x\\\\15^{-2}=15^x\\\\x=-2$