document.write( "Question 599291: log base 2 of (x-5) - log base 2 of (x+2) = 3 \n" ); document.write( "

Algebra.Com's Answer #378903 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
The key is to express $\"+3+\"$ as a log to the base $\"+2+\"$
\n" ); document.write( " $\"+log%28+2%2C+x+%29+=+3+\"$
\n" ); document.write( " $\"+log%28+2%2C+8+%29+=+3+\"$
\n" ); document.write( " $\"+log%28+2%2C+x-5+%29+-+log%28+2%2C+x%2B2+%29+=+log%28+2%2C+8+%29+\"$
\n" ); document.write( "Use the rule:
\n" ); document.write( " $\"+log%28a%29+-+log%28b%29+=+log%28a%2Fb%29+\"$
\n" ); document.write( " $\"+log%28+2%2C+%28+x-5+%29%2F%28+x%2B2+%29+%29+=+log%28+2%2C8+%29+\"$
\n" ); document.write( " $\"+%28+x-5+%29+%2F+%28+x%2B2+%29+=+8+\"$
\n" ); document.write( " $\"+x+-+5+=+8%2A%28+x+%2B+2+%29+\"$
\n" ); document.write( " $\"+x+-+5+=+8x+%2B+16+\"$
\n" ); document.write( " $\"+7x+=+-21+\"$
\n" ); document.write( " $\"+x+=+-3+\"$
\n" ); document.write( "check:
\n" ); document.write( " $\"+log+%282%2C+%28x-5%29%29+-+log+%282%2C%28x%2B2%29+%29+=+3+\"$
\n" ); document.write( " $\"+log+%282%2C%28-8%29+%29+-+log+%282%2C%28-1%29+%29+=+3+\"$
\n" ); document.write( " $\"+log%28+2%2C+%28-8%29%2F%28-1%29+%29+=+3+\"$
\n" ); document.write( " $\"+log%28+2%2C8+%29+=+3+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( "
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