Verified answer

Hello

Use logs ( but you will not need a calculator )

log [25^(z-4)]= log (125)

(z - 4) log (25) = log (125)

(z - 4) = log (125) / log (25)

But :

log (125) = log (5^3) = 3 log (5)

log (25) = log (5^2) = 2 log (5)

So log (125) / log (25) = 3 log (5) / 2 log (5) = 3/2 = 1.5

And (z - 4) = 1.5 ===> z = 4 + 1.5 = 5.5 ===> Answer A

Hope it helps

Bye !

Try to get a common base. Notice that 25 is 5^2 and 125 is 5^3, this gives:

(5^2)^(z - 4) = 5^3

Recall, when you raise a power to another power, you multiply them...so we have 2(z - 4) = 2z - 8

5^(2z - 8) = 5^3

Once they have the same bases, simply cancel them out and deal with only the powers:

2z - 8= 3 --> Add 8 to both sides.

2z = 11 --> Divide through by 2.

ANSWER: z = 5.5

Hope that helps!

5.5