Use the OnetoOne Property to solve the equation for x ex2 6

Use the One-to-One Property to solve the equation for x. e^x2 - 6 = e^5x

Solution

As per the one to one property of exponential functions, if a^m = aⁿ and if a > 0 and a is not equal to 1, then m = n.

Thus, x² -6  = 5x ( as e > 0 and e is not equal to 1) or, x² -5x - 6 = 0 or, x² - 6x + x - 6 = 0 or, x (x - 6) + 1 ( x- 6) = 0

or, ( x + 1)( x -6) = 0 Thus, x = 6 or -1.