Question

Sendo log a2=20〗 e log a3〖3=30〗, calcule o valor de log_a100

Answer 1

$\log_a(100)=\log_a(2^2\cdot5^2)\\ \log_a(100)=\log(2)^2+\log(5)^2\\ \log_a(100)=2\cdot\log(2)+\log\left( \dfrac{10}{2}\right)^2\\\\ \log_a(100)=2\cdot\log(2)+[\log(10)-\log(2)]^2\\ \log_a(100)=2\cdot\log(2)+2\cdot[\log_{10}(10)-\log(2)]\\ \log_a(100)=2\cdot20+2\cdot(1-20)\\ \log_a(100)=40+2\cdot(-19)\\ \log_a(100)=40-38\\\\ \Large\boxed{\log_a(100)=2}$