<PRE><B>Question 892606</B>
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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