document.write( "Question 1198977: solve for x: 1+log2(x^2-4x-16)=log2(x^2-3x+4) \n" ); document.write( "

Algebra.Com's Answer #832670 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( " $\"1%2Blog%282%2C%28x%5E2-4x-16%29%29=log%282%2C%28x%5E2-3x%2B4%29%29\"$

\n" ); document.write( "Rewrite the first term on the left as a base 2 logarithm.

\n" ); document.write( " $\"log%282%2C%282%29%29%2Blog%282%2C%28x%5E2-4x-16%29%29=log%282%2C%28x%5E2-3x%2B4%29%29\"$

\n" ); document.write( "Use the rule for adding logarithms with the same base.

\n" ); document.write( " $\"log%282%2C%282%28x%5E2-4x-16%29%29%29=log%282%2C%28x%5E2-3x%2B4%29%29\"$

\n" ); document.write( " $\"log%282%2C%282x%5E2-8x-32%29%29=log%282%2C%28x%5E2-3x%2B4%29%29\"$

\n" ); document.write( "Set the arguments equal to each other and solve the resulting quadratic equation.

\n" ); document.write( " $\"2x%5E2-8x-32=x%5E2-3x%2B4\"$
\n" ); document.write( " $\"x%5E2-5x-36=0\"$
\n" ); document.write( " $\"%28x-9%29%28x%2B4%29=0\"$
\n" ); document.write( " $\"x=9\"$ or $\"x=-4\"$

\n" ); document.write( "Both values satisfy the original equation, so

\n" ); document.write( "ANSWERS: x = 9 or x = -4

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