Question

sendo a² + b² = 70ab, calcule log5 (a+b)²/ab em função de m = log5 2 e n = log5 3.

Answer 1

(a + b)² = a² + b² + 2ab 
 a² + b² = 70ab
(a + b)² = 70ab = 2ab = 72ab
(a + b)²/ab = 72ab/ab = 72
72 = 2³ . 3²
log5(72) = 3log5(2) + 2log5(3) = 3m + 2n
espero ter ajudado.

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{a^2 + b^2 = 70ab}$

$\mathsf{m = log_5\:2}$

$\mathsf{n = log_5\:3}$

$\mathsf{log_5\left(\dfrac{(a + b)^2}{ab}\right) = x}$

$\mathsf{log_5\left(\dfrac{a^2 + 2ab + b^2}{ab}\right) = x}$

$\mathsf{log_5\left(\dfrac{70ab + 2ab}{ab}\right) = x}$

$\mathsf{log_5\left(\dfrac{70 + 2}{1}\right) = x}$

$\mathsf{log_5\:72 = log_5\:(8.9)}$

$\mathsf{log_5\:72 = log_5\:(2^3.3^2)}$

$\mathsf{log_5\:72 = 3\:log_5\:2 + 2\:log_5\:3)}$

$\boxed{\boxed{\mathsf{log_5\left(\dfrac{(a + b)^2}{ab}\right) = 3m + 2n}}}$