Question

Se log p (p^2 q^2) =5, entao logq p e igual a

Answer 1

Propriedades utilizadas:

$log(ab) = log(a) + log(b) \\\\ log_a(b) = { 1 \over log_b(a)} \\\\ log(a^b) = blog(a)$

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$log_p(p^2q^2) = 5 \\\\ log_p(p^2) + log_p(q^2) = 5 \\\\ 2log_p(p) + 2log_p(q) = 5 \\\\ 2( 1 + log_p(q) ) = 5 \\\\ log_p(q) = { 5 \over 2} - 1 \\\\ log_p(q) = { 3 \over 2} \\\\ { 1 \over log_q(p) } = { 3 \over 2} \\\\ \boxed{ log_q(p) = { 2 \over 3} }$