Question

sendo log 2=a e log 3=b calcule log 180

Answer 1

Olá Isabelle,

use as propriedades..

$\log_x(y)^n\Rightarrow n\cdot\log_x(y)\\\\ \log(xy)\Rightarrow \log(x)+\log(y)\\\\\log\left(\dfrac{x}{y}\right)\Rightarrow \log(x)-\log(y)\\\\\log_y(y)=1$

$\log(180)=\log(2^2\cdot3^2\cdot5)\\ \log(180)=\log(2)^2+\log(3)^2+\log(5)\\ \log(180)=2\cdot\log(2)+2\cdot\log(3)+\log\left( \dfrac{10}{2}\right)\\ \log(180)=2\cdot\log(2)+2\cdot\log(3)+[\log(10)-\log(2)]\\ \log(180)=2\cdot\log(2)+2\cdot\log(3)+[\log_{10}(10)-\log(2)]\\ \log(180)=2\cdot a+2\cdot b+(1-a)\\ \log(180)=2a+2b+1-a\\\\ \Large\boxed{\log(180)=a+2b+1}$

Tenha ótimos estudos ;D