document.write( "Question 1096402: prove that : \"25%5E%28log8%29%2A8%5E%28log4%29\"\"%22%22=%22%22\"\"64\"
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Algebra.Com's Answer #710811 by Edwin McCravy(20063)\"\" \"About 
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document.write( "Prove:\r\n" );
document.write( "\"25%5E%28log%28%288%29%29%29%2A8%5E%28log%28%284%29%29%29\"\"%22%22=%22%22\"\"64\"\r\n" );
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document.write( "Start with the left side and show that it equals 64\r\n" );
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document.write( "\"25%5E%28log%28%288%29%29%29%2A8%5E%28log%28%284%29%29%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "Write 5 as 5², 8 as 2³, and 4 as 2²\r\n" );
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document.write( "\"%285%5E2%29%5E%28log%28%282%5E3%29%29%29%2A%282%5E3%29%5E%28log%28%282%5E2%29%29%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "Use the rule of logarithms that allows an exponent of what\r\n" );
document.write( "a log is taken of to be moved out front as a coefficient of\r\n" );
document.write( "the logarithm. \r\n" );
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document.write( "\"%285%5E2%29%5E%283log%28%282%29%29%29%2A%282%5E3%29%5E%282log%28%282%29%29%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "Use the rule of exponents that says that when a power\r\n" );
document.write( "is raised to a power, we multiply the exponents\r\n" );
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document.write( "\"5%5E%286log%28%282%29%29%29%2A2%5E%286log%28%282%29%29%29%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "Use the rule that says if the product of two powers\r\n" );
document.write( "have the same exponent, we can multiply the bases\r\n" );
document.write( "and use the common exponent. \r\n" );
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document.write( "\"%285%2A2%29%5E%286log%28%282%29%29%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "use 5×2 = 10\r\n" );
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document.write( "\"10%5E%286log%28%282%29%29%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "Use the rule that says that a coefficient of a logarithm\r\n" );
document.write( "can be moved to the exponent of what the logarithm is taken of:\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C10%5E%28log%28%282%5E6%29%29%29%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "Use the definition of \"log(26)\", which is \"the power to which\r\n" );
document.write( "10 must be raised to give 26\".  Since 10 here is\r\n" );
document.write( "raised to that power, its value must be 26.\r\n" );
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document.write( "\"2%5E6\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"64\"\r\n" );
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document.write( "proved\r\n" );
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document.write( "Edwin
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