Question

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

Answer 1

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