Error: The bases need to be the same before applying the Property of Equality for Exponential Functions. Solution: x=- 18
Practice makes perfect
Finding the Error
Let's start by determining where the error occurred. Let's look at the first step.
5^(3x+2)&=25^(x-8)
&⇓ *
3x+2&=x-8
The error occurred when going from the first line to the second line; there is an incorrect application of the Property of Equality for Exponential Equations.
b^x&=b^y
&⇓
x&=y
This property can only be applied whenever the bases are the same, and in our case the bases were not.
Correctly Solving the Equation
In order to correctly solve this equation, we need to make sure that the bases are equal. To do this we will rewrite 25 as 5^2 and simplify.
