Question

Which of the following is the solution to the equation 25^(z − 2) = 125?

z = 5.5
z = 3.5
z = −2.5
z = −0.5
I thought it would've been -2.5, but when I did the math I got POSITIVE 2.5, so I'm kinda stuck :/

Answer 1

The answer is z=3.5

Explanation:

I'm not sure how you solved it but here is what I did:

25^(z-2)=125

Get the same base for both

(5²)⁽ˣ⁻²⁾=5³

Then you apply the exponent rule to combine

5²ˣ⁻⁴=5³

Since the bases are the same the exponents have to be the same thus:

2x-4=3

2x=7

x=7/2

x=3.5

I hope this helps :)