Question

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

Answer 1

Answer:

z = $\frac{11}{2}$

Step-by-step 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 = $\frac{11}{2}$ ( = 5.5 )

Answer 2

Answer:

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