Question 892606: Solve 125^x=5
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! start with 125^x = 5
take the log of both sides of this equation to get:
log(125^x) = log(5)
since log(125^x) = x * log(125), your equation becomes:
x * log(125) = log(5)
divide both sides of this equation by log(125) to get:
x = log(5) / log(125)
use the log function of your calculator to get:
x = .3333333........
this is the same as x = 1/3
your original equation of 225^x = 5 becomes 225^(1/3) = x
since 225^(1/3) = the cube root of 125, your equation becomes:
cube root (125) = 5
since cube root (125) = 5 because 5^3 = 125, your equation becomes:
5 = 5
this confirms the solution is correct.
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