Question

6(4^x+9^x)=13×6^x then find the value of 'x'

Answer 1

$dividing \: throughout \: by \: {6}^{x } \\ 6( {( \frac{2}{3} )}^{x} + {( \frac{3}{2}) }^{x} ) = 13 \\ let \: y = {( \frac{2}{3} )}^{x} . \: equation \: becomes \\ 6(y + \frac{1}{y} ) = 13 \\ 6 {y}^{2} - 13y + 6 = 0 \\ 6 {y}^{2} - 9y - 4y + 6 = 0 \\ 3y(2y - 3) - 2(2y - 3) = 0 \\ (3y - 2)(2y - 3) = 0 \\ y = \frac{2}{3} \: or \: \frac{3}{2} \\ {( \frac{2}{3} )}^{x} = \frac{2}{3} \: \: gives \: x = 1 \\ {( \frac{2}{3} )}^{x} = \frac{3}{2} \: \: gives \: x = - 1$

Answer 2

Step-by-step explanation:

This is the proper way to do this sum