Solve the equation 274x9x1 xSolutionWe are given 274x 9x 1

Solve the equation

27^4x=9^x+1

^x=

Solution

We are given 27^4x = 9^{(x + 1)}. Therefore, (3³)^4x = (3²)^{(x + 1)} or, 3^12x = 3^{(2x + 2)}   so that 12x = 2x + 2 or, 10x = 2 . Therefore x = 1/5.