document.write( "Question 106845: Could you please take the time to help me solve this problem: Solve g(x) = 0 for x, if g(x) = log x + log x2 + 8 log x – log x3 – 16. Note that all logarithmic functions are to the base 10. Show your work.\r
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Algebra.Com's Answer #77747 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve g(x) = 0 for x, if
\n" ); document.write( " $\"g%28x%29=log%28%28x%29%29%2B8%2Alog+x%2Blog%28%28x%5E2%29%29-log%28%28x%5E3%29%29-16\"$
\n" ); document.write( "The original equation is re-written to group like terms.
\n" ); document.write( "Here are the logarithm rules for reference
\n" ); document.write( " $\"log%28%28a%29%29%2Blog%28%28b%29%29=log+%28%28ab%29%29\"$
\n" ); document.write( " $\"log%28%28a%29%29-log%28%28b%29%29=log+%28%28a%2Fb%29%29\"$
\n" ); document.write( " $\"k+log%28%28a%29%29+=+log%28%28a%5Ek%29%29\"$
\n" ); document.write( "Now let's appply the rules to your equation,
\n" ); document.write( " $\"g%28x%29=log%28%28x%29%29%2B8%2Alog+x%2Blog%28%28x%5E2%29%29-log%28%28x%5E3%29%29-16\"$
\n" ); document.write( " $\"g%28x%29=9%2Alog%28%28x%29%29%2Blog%28%28x%5E2%29%29-log%28%28x%5E3%29%29-16\"$
\n" ); document.write( " $\"g%28x%29=log%28%28x%5E9%29%29%2Blog%28%28x%5E2%29%29-log%28%28x%5E3%29%29-16\"$
\n" ); document.write( " $\"g%28x%29=log%28%28x%5E9%2A%28x%5E2%29%2Fx%5E3%29%29-16\"$
\n" ); document.write( " $\"g%28x%29=log%28%28x%5E%289%2B2-3%29%29%29-16\"$
\n" ); document.write( " $\"g%28x%29=log%28%28x%5E%288%29%29%29-16\"$
\n" ); document.write( "When g(x)=0, then
\n" ); document.write( " $\"0=log%28%28x%5E%288%29%29%29-16\"$
\n" ); document.write( " $\"log%28%28x%5E%288%29%29%29=16\"$
\n" ); document.write( " $\"x%5E8=10%5E16\"$
\n" ); document.write( " $\"x%5E8=%2810%5E2%29%5E8\"$
\n" ); document.write( " $\"x=%2810%5E2%29\"$
\n" ); document.write( " $\"highlight%28x=100%29\"$
\n" ); document.write( "Check your answer
\n" ); document.write( " $\"g%28x%29=log%28%28x%29%29%2B8%2Alog+x%2Blog%28%28x%5E2%29%29-log%28%28x%5E3%29%29-16\"$
\n" ); document.write( " $\"g%28100%29=+log%28100%29%2B8%2Alog%28100%29%2Blog%28100%5E2%29-log%28100%5E3%29-16\"$
\n" ); document.write( " $\"0=2%2B8%2A2%2B4-6-16\"$
\n" ); document.write( " $\"0=0\"$
\n" ); document.write( "Good answer. \n" ); document.write( "

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