Question

What is the following is the solution to the equation 25^(z+2) = 125

Answer 1

First, rewrite the equation $25^{z+2} = 125$ with the base equal to 5. Note that:

• $25=5^2;$
• $125=5^3;$
• $25^{z+2}=(5^2)^{z+2}=5^{2\cdot (z+2)}.$

Then

$5^{2\cdot (z+2)}=5^3.$

Since the bases are equal, you have that powers are equal too:

$2\cdot (z+2)=3,\\ \\2z+4=3,\\ \\2z=3-4,\\ \\2z=-1,\\ \\z=-\dfrac{1}{2}.$

Answer: $z=-\dfrac{1}{2}.$