Question

find x if 5^x-2 × 5^x-4 = 135

Answer 1

We have,     5x−2 × 32x − 3 = 135⇒5x−2 × 32x − 3 = 3×3×3×5⇒5x−2 × 32x − 3 = 51 × 33On equating the powers of 5 on both sides, we get     x − 2 = 1⇒x = 1 + 2⇒x = 3On equating the powers of 3 on both sides, we get     2x − 3 = 3⇒2x = 3 + 3⇒2x = 6⇒x = 62⇒x = 3Hence, x = 3 is the solution.