Solve the following exponential equation by expressing each

Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents. 8^x+5=32^x9

Solution

We have 8^x+5 =32^x-9 or, (2³)^x+5 = (2⁵ )^x-9 or, 2^3x+15 =2^5x-45. Hence, 3x+15 = 5x -45 or, 5x-3x = 15+45 or, 2x = 60 so that x = 60/2 =30.