document.write( "Question 889692: Find the value of a:
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Algebra.Com's Answer #538369 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"log%28a%2C%281%2F25%29%29\"\"%22%22=%22%22\"\"-2%2F3\"\r\n" );
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document.write( "Use the rule:\r\n" );
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document.write( "\"log%28x%2C%28y%29%29\"\"%22%22=%22%22\"\"z\" is equivalent to \"x%5Ez\"\"%22%22=%22%22\"\"y\".\r\n" );
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document.write( "\"log%28a%2C%281%2F25%29%29\"\"%22%22=%22%22\"\"-2%2F3\" is equivalent to \r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2Ca%5E%28-2%2F3%29%29\"\"%22%22=%22%22%29\"\"1%2F25\".\r\n" );
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document.write( "We want to make the exponent of a become 1.  To do that we raise\r\n" );
document.write( "both sides to the \"-3%2F2\" power, the reciprocal of the power\r\n" );
document.write( "to which a is now raised to:\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2C%28a%5E%28-2%2F3%29%29%5E%28-3%2F2%29%29\"\"matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29%29\"\"matrix%282%2C1%2C%22%22%2C%281%2F25%29%5E%28-3%2F2%29%29\"\r\n" );
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document.write( "Multiply those exponents and get a to the 1 power:\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2Ca%5E1%29\"\"matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29%29\"\"matrix%282%2C1%2C%22%22%2C%281%2F25%29%5E%28-3%2F2%29%29\"\r\n" );
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document.write( "That's technically the answer but we need to simplify it:\r\n" );
document.write( "We write 25 as \"5%5E2\".\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2Ca%29\"\"matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29%29\"\"matrix%282%2C1%2C%22%22%2C%281%2F%285%5E2%29%29%5E%28-3%2F2%29%29\"\r\n" );
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document.write( "We write \"1%2F5%5E2\" as \"5%5E%28-2%29\"\r\n" );
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document.write( "\"matrix%282%2C1%2C%22%22%2Ca%29\"\"matrix%282%2C1%2C%22%22%2C%22%22=%22%22%29%29\"\"matrix%282%2C1%2C%22%22%2C%285%5E%28-2%29%29%5E%28-3%2F2%29%29\"\r\n" );
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document.write( "Multiply those exponents:  \"%28-2%29%28-3%2F2%29\"\"%22%22=%22%22\"\"3\"\r\n" );
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document.write( "\"a\"\"%22%22=%22%22\"\"5%5E3\"\r\n" );
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document.write( "\"a\"\"%22%22=%22%22\"\"125\"\r\n" );
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document.write( "Edwin
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