document.write( "Question 855564: Prove that each statement is true.
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Algebra.Com's Answer #515466 by Edwin McCravy(20081)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "To prove: \"log%288%2C59%29=log%2810%2C59%29%2Flog%2810%2C8%29\"\r\n" );
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document.write( "Here goes:\r\n" );
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document.write( "Let \"log%288%2C59%29=x\"\r\n" );
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document.write( "Change that log equation to its \r\n" );
document.write( "equivalent exponent form:\r\n" );
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document.write( "\"8%5Ex=59\"\r\n" );
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document.write( "Now take logs base 10 of both sides:\r\n" );
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document.write( "\"8%5Ex=59\"\r\n" );
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document.write( "\"log%2810%2C8%5Ex%29=log%2810%2C59%29\"\r\n" );
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document.write( "Use the \"jump-over\" rule of logarithms where the exponent\r\n" );
document.write( "\"jumps over both its base and the word \"log\" and turns into a\r\n" );
document.write( "multiplier. Like this:\r\n" );
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document.write( "\"x%2Alog%2810%2C8%29=log%2810%2C59%29\"\r\n" );
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document.write( "See how the x jumped over the \"8\" and the \"log\" and became\r\n" );
document.write( "a multiplier instead of being an exponent. \r\n" );
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document.write( "Now we divide both sides by \"log%2810%2C8%29\" to solve for x.\r\n" );
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document.write( "\"x=log%2810%2C59%29%2Flog%2810%2C8%29\"\r\n" );
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document.write( "And now we go back and remember what x was -- we let \"log%288%2C59%29=x\"\r\n" );
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document.write( "So we have:\r\n" );
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document.write( "\"log%288%2C59%29=log%2810%2C59%29%2Flog%2810%2C8%29\"\r\n" );
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document.write( "and it's proved.\r\n" );
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document.write( "Edwin

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