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=-(1)/(2).`

Answer:
`z=-(1)/(2).`