SOLUTION: How do you solve 25^(x+5)=125^(x+4) I think you are supposed to use the change of base formula? I keep getting confused when I take the log of both sides. Hope you can help. Thanks

Question 57683: How do you solve 25^(x+5)=125^(x+4) I think you are supposed to use the change of base formula? I keep getting confused when I take the log of both sides. Hope you can help. Thanks
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
The easiest way to solve this is to change the bases before you take the logs:
25=5^2, and 125=5^3
Now that their bases are the same you can equate their exponents:
2(x+5)=3(x+4)
2x+10=3x+12
2x-2x+10=3x-2x+12
10=x+12
10-12=x+12-12
-2=x
Check:

We're right.
:
Since you asked to take the logs of both sides, I will show you that method, but it ain't gonna be pretty.

You'll need a scientific calculator here. The other way didn't require one.

:
Whatever makes your teacher happy.
Happy Calculating!!!
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