Question

find'x' 2log_5x = 1+log_5(x-6/5)​

Answer 1

Answer:

x = 2 and x = 3

Step-by-step explanation:

Formulas used :

$log_5 \ 5 = 1$

$log_5 \ x + log_5 \ y = log_5 \ (xy)$

$log_5 \ x = log_5 \ y => x = y$

Steps :

$2 \ log_5 \ x = 1 + log_5 (x - \frac{6}{5} )\\\\2 \ log_5 \ x = log_5 \ 5+ log_5 (x - \frac{6}{5} )\\\\2 \ log_5 \ x = log_5 \ ( 5(x - \frac{6}{5} ))\\\\x^2 = 5(x - \frac{6}{5})\\\\x^2 = 5x - 6\\\\x^2 - 5x + 6 = 0\\\\x^2 - 2x - 3x + 6 = 0\\\\x(x - 2 ) - 3 (x - 2) = 0\\\\(x - 3)(x-2) = 0\\\\x = 3 , x = 2$