SOLUTION: Solve 125^x=5

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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