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

Question

asked Jul 10, 2019 199k views

1 Answer

Opsidao · Answer 1 · 2019-07-17T04:44:27+0000

Answer:

z = -0.5

Explanation:

Using exponent rule:

x^a = x^b then a = b

Given the equation:

25^(z+2) = 125

We can write 25 and 125 as:

$25 = 5 \cdot 5 = 5^2$

$125 = 5 \cdot 5 \cdot 5 = 5^3$

then;

5^(2(z+2))= 5^3

Apply the rule:

2(z+2) = 3

using distributive property
$a \cdot (b+c) = a\cdot b+ a\cdot c$

2z+4 = 3

Subtract 4 from both sides we have;

2z = -1

Divide both sides by 2 we have;

z = -0.5

Therefore, the solution for the given equation is, z = -0.5