Question

1 Usando a definição de logaritmo, determine o valor de m em casa item​

Answer 1

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$\tt a)~\sf\ell og_381=m\\\sf 3^m=81\\\sf 3^m=3^4\\\huge\boxed{\boxed{\boxed{\boxed{\sf m=4}}}}$

$\tt b)~\sf\ell og_{\sqrt{7}}m=2\\\sf m=(\sqrt{7})^2\\\huge\boxed{\boxed{\boxed{\boxed{\sf m=7}}}}$

2)

$\tt a)~\sf\ell og_{100}0,001=\ell og_{10^2}10^{-3}=-\dfrac{3}{2}\\\tt b)~\sf 0,125=\dfrac{125\div125}{1000\div125}=\dfrac{1}{8}=2^{-3}\\\sf\ell og_20,125=\ell og_22^{-3}=\dfrac{-3}{1}=-3$

3)

$\sf\ell og_26=log_2(2\cdot3)\\\sf=\ell og_22+\ell og_23=1+1,585=2,585$