52x 55x 36 52x 55x 36Solution52x 55x 36 ie 52x 55x 3

Solution

5^2x - 5(5^x) = 36

ie. (5)^2x - 5(5)^x - 36 = 0

let (5)^x = y

so, equation can be re-written as y² - 5y - 36 = 0

hence, (y-9)(y+4) = 0

so, y = 9 or y = -4

Now, since y = (5)^x , so, it can\'t be negative.

Hence, y = 9

so, (5)^x = 9

so, x = log₅(9)