Question

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

5.5
3.5
-2.5
-0.5

Answer 1

If that z is up there as an exponent, we need a way to bring it down to the level of the other numbers so we can work with it. We can't do anything with it up there. We need to use the rules of logs here. Take the log of both sides to get
`log(25) ^(z+2) =log(125)`. Now that we've taken the log of both sides, the rule says we can bring down the exponent in front, like this:
`(z+2)log(25)=log(125)`. We will divide both sides by log(25) to get this:
`z+2= (log(125))/(log(25))` and subtract the 2 to isolate z:
`z= (log(125))/(log(25))-2`. We will do the division on our calculators and then subtract 2 from that to get a z value of -0.5, last choice above.