Answer:
z = -0.5
Step-by-step explanation:
Using exponent rule:
[tex]x^a = x^b[/tex] then a = b
Given the equation:
[tex]25^{z+2} = 125[/tex]
We can write 25 and 125 as:
[tex]25 = 5 \cdot 5 = 5^2[/tex]
[tex]125 = 5 \cdot 5 \cdot 5 = 5^3[/tex]
then;
[tex]5^{2(z+2)}= 5^3[/tex]
Apply the rule:
[tex]2(z+2) = 3[/tex]
using distributive property [tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]
[tex]2z+4 = 3[/tex]
Subtract 4 from both sides we have;
[tex]2z = -1[/tex]
Divide both sides by 2 we have;
z = -0.5
Therefore, the solution for the given equation is, z = -0.5
