Question

Sendo logª2 =20 , logª 5=30, Calcule logª 200

Answer 1

$\Large\boxed{\begin{array}{l}\sf\ell og_a2=20~~\ell og_a5=30\\\sf \ell og_a200=?\\\begin{array}{c|c}\sf200&\sf2\\\sf100&\sf2\\\sf50&\sf2\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 200=2^3\cdot5^2\\\sf \ell o_a200=\ell og_a(2^3\cdot 5^2)\\\sf\ell og_a200=\ell og_a2^3+\ell og_a5^2\\\sf\ell og_a200=3\ell og_a2+2\ell og_a5\\\sf \ell og_a200=3\cdot20+2\cdot30\\\sf \ell og_a200=60+60\\\huge\boxed{\boxed{\boxed{\boxed{\sf\ell og_a200=120}}}}\end{array}}$

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_a\:2 = 20}$

$\mathsf{log_a\:5 = 30}$

$\mathsf{log_a\:200 = log_a\:(2^3.5^2)}$

$\mathsf{log_a\:200 = 3\:log_a\:2 + 2\:log_a\:5}$

$\mathsf{log_a\:200 = 3(20) + 2(30)}$

$\mathsf{log_a\:200 = 60 + 60}$

$\boxed{\boxed{\mathsf{log_a\:200 = 120}}}$