Question

Which of the following is the solution to the equation 25^(z − 4) = 125? (6 points)

Answer 1

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Answer 2

z =
`(11)/(2)`

Explanation:

Using the rule of exponents

`(a^m)^(n)` =
`a^(mn)` , then

`25^(z-4)` = 125 [ 25 = 5² and 125 = 5³ ]

`(5^2)^(z-4)` = 5³

`5^(2z-8)` = 5³

Since the bases on both sides are equal, both 5, then equate the exponents

2z - 8 = 3 ( add 8 to both sides )

2z = 11 ( divide both sides by 2 )

z =
`(11)/(2)` ( = 5.5 )