Example Question - equal bases

Solving Exponential Equations with Equal Bases

To solve the equation e^(2x) = e^(3x-1), we will use the property that if two exponents with the same base are equal, then their exponents must be equal as well. This means we can set the exponents equal to each other and solve for x. 2x = 3x - 1 Now, let's solve for x: 2x - 3x = -1 -x = -1 Multiply both sides by -1 to isolate x: x = 1 So, the solution to the equation is x = 1.