Question

Se 10^x = 50^y, atribuindo 0,7 para log 5, então o valor de 6. (x/y)^2 é:

Answer 1

Resposta:

6. (x/y)^2 = 17,34

Explicação passo a passo:

Log 5 = 0,7

Lembrando que log 10 = 1

e que log (a.b) = log a + log b

10^x = 50^y

log 10^x = log 50^y

x.log 10 = y.log 50

x . 1 = y.log (10.5)

x = y.(log 10 + log 5)

x = y.(1 + 0,7)

x = y.(1,7)

x/y = 1,7

6.(x/y)^2 =

6. (1,7)^2 =

6 . 2,89 =

17,34

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf 10^x = 50^y$

$\sf log\:10^x = log\:50^y$

$\sf \dfrac{x}{y} = \dfrac{log\:50}{log\:10}$

$\sf 6\:.\:\left(\dfrac{x}{y}\right)^2 = 6\:.\:\left(\dfrac{log\:50}{log\:10}\right)^2$

$\sf 6\:.\:\left(\dfrac{x}{y}\right)^2 = 6\:.\:\left(\dfrac{log\:5 + log\:10}{log\:10}\right)^2$

$\sf 6\:.\:\left(\dfrac{x}{y}\right)^2 = 6\:.\:\left(\dfrac{0,7 + 1}{1}\right)^2$

$\sf 6\:.\:\left(\dfrac{x}{y}\right)^2 = 6\:.\:(1,7)^2$

$\boxed{\boxed{\sf 6\:.\:\left(\dfrac{x}{y}\right)^2 = 17,34}}$