document.write( "Question 1156475: Solve the equation without using a calculator. (Enter your answers as a comma-separated list.)
\n" ); document.write( "log(x^3) = (log x)^2 \n" ); document.write( "

Algebra.Com's Answer #779171 by Shin123(626) $\"\"$ $\"About$

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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). \n" ); document.write( "

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