Question

log 2 = 20 log de 5 = 30 calcule log 100

Answer 1

Primeiro vamos tirar o m.m.c 100 = 2² . 5²

log 2².5² = log 2² + log 5²

2 log 2 + 2 log 5 = 2.20 + 2.30 = 100

O log de 100 = 100

Answer 2

$\log100=\log(5^2\cdot2^2)\\ \log100=\log(5^2)+\log(2^2)\\ \log100=\log(5)^2+\log(2^2)\\ \log100=2\cdot\log(2)+2\cdot\log(5)\\\\ \log2=20~~e~~\log5=30~~~lembra!?\\\\ \log100=2\cdot20+2\cdot30\\ \log100=40+60\\\\ \Large\boxed{\log100=100}$

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