SOLUTION: Solve the equation without using a calculator. (Enter your answers as a comma-separated list.) log(x^3) = (log x)^2

Algebra ->  Equations -> SOLUTION: Solve the equation without using a calculator. (Enter your answers as a comma-separated list.) log(x^3) = (log x)^2      Log On


   

Question 1156475: Solve the equation without using a calculator. (Enter your answers as a comma-separated list.)
log(x^3) = (log x)^2
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Since log%28x%5E3%29=3%2Alog%28x%29, the equation turns into 3%2Alog%28x%29=%28log%28x%29%29%5E2. Letting y=log(x) gets 3y=y%5E2. Moving everything to one side gives y%5E2-3y=0. Factoring gives y%28y-3%29=0. So y=0 or y=3. If y=0, then x=1. If y=3, the answer depends on what base you are using. Assuming a base of 10, x=1000. So the solution is (1,1000). If the base is some arbitrary number n, then the answer will be (1,n3).