Exercise 51 Page 304

Let's start by reviewing what the Property of Equality for Exponential Equations says. This property states that two powers with a common base are equal if and only if their exponents are equal as well. This allows us to equate exponents and to solve exponential equations involving powers with the same base. An example is shown below. 4^(x+1) = 4^4 ⇔ x+1 = 4 However, recall that a power with a base of 1 is always equal to 1, even if their exponents are different. 1^3 = 1 1^8=1 ⇓ 1^3 =1^8 In the example above we can see that 1^3 =1^8, even if 3 ≠ 8. This is why the Property of Equality for Exponential Equations is only valid for a power with a base different from 1.