document.write( "Question 1113137: Please help me. How to prove that log b x- log b y = log b (x/y). (* \"b\" should be smaller letter)
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Algebra.Com's Answer #728183 by math_helper(2461)\"\" \"About 
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The property of exponents \"+x%5Ea%2Fx%5Eb++=+x%5E%28a-b%29+\" (*) will be used. This can be easily proved.\r
\n" ); document.write( "\n" ); document.write( "Let \"log%28b%2C%28x%2Fy%29%29+=+w+\" <—> \"+b%5Ew+=+x%2Fy+\" (1)
\n" ); document.write( "Let \"+log%28b%2C%28x%29%29+=+v+\" <—> \"+b%5Ev+=+x+\" (2)
\n" ); document.write( "Let \"+log%28b%2C%28y%29%29+=+z+\" <—> \"+b%5Ez+=+y+\" (3)\r
\n" ); document.write( "\n" ); document.write( "\"+b%5Ew+=+x%2Fy+=+b%5Ev%2Fb%5Ez+=+b%5E%28v-z%29+\" (property (*) used on last step)\r
\n" ); document.write( "\n" ); document.write( "Picking off just this part:
\n" ); document.write( "\"+x%2Fy+=+b%5E%28v-z%29+\"\r
\n" ); document.write( "\n" ); document.write( "and taking log base b of both sides:
\n" ); document.write( "\"+log%28b%2C%28x%2Fy%29%29+=+log%28b%2C%28b%5E%28v-z%29%29%29+=+v-z+\" \r
\n" ); document.write( "\n" ); document.write( "Substituting (2) and (3) for v and z, respectively, completes the proof:
\n" ); document.write( "\"+log%28b%2C%28x%2Fy%29%29=+log%28b%2C%28x%29%29+-+log%28b%2C%28y%29%29+\"
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