document.write( "Question 148642: log(base6)(b^2 + 2) + log(base6)2 = 2\r
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\n" ); document.write( "\n" ); document.write( "log(base3)(5x+5) - log(base3)(x2 - 1) = 0\r
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Algebra.Com's Answer #108987 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
\"log%286%2C%28b%5E2+%2B+2%29%29+%2B+log%286%2C%282%29%29+=+2+\"
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document.write( "Use this principle of logs on the left:\"log%28N%2C%28X%29%29+%2B+log%28N%2C%28Y%29%29+=+log%28N%2C%28X%2AY%29%29\"\r\n" );
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document.write( "\"log%286%2C%28%28b%5E2+%2B+2%29%2A2%29%29+=+2+\"\r\n" );
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document.write( "\"log%286%2C%282%2A%28b%5E2+%2B+2%29%29%29+=+2+\"\r\n" );
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document.write( "\"log%286%2C%282b%5E2+%2B+4%29%29+=+2+\"\r\n" );
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document.write( "Now use this principle of logs on that equation:\r\n" );
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document.write( "The log equation \"log%28N%2CX%29=Y\" can be rewritten \r\n" );
document.write( "as the exponential equation \"X=N%5EY\"\r\n" );
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document.write( "\"2b%5E2%2B4+=+6%5E2\"\r\n" );
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document.write( "\"2b%5E2%2B4+=+36\"\r\n" );
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document.write( "Subtract \"4\" from both sides:\r\n" );
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document.write( "\"2b%5E2=32\"\r\n" );
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document.write( "Divide both sides by 2\r\n" );
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document.write( "\"%282b%5E2%29%2F2=32%2F2\"\r\n" );
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document.write( "\"b%5E2=16\"\r\n" );
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document.write( "Subtract 16 from both sides:\r\n" );
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document.write( "\"b%5E2-16=0\"\r\n" );
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document.write( "Factor the left side:\r\n" );
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document.write( "\"%28b-4%29%28b%2B4%29=0\"\r\n" );
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document.write( "Set each factor = 0\r\n" );
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document.write( "\"b-4=0\" gives solution \"b=4\"\r\n" );
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document.write( "\"b%2B4=0\" gives solution \"b=-4\" \r\n" );
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document.write( "and \r\n" );
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document.write( "\"log%283%2C%285x%2B5%29%29+-+log%283%2C%28x%5E2+-+1%29%29+=+0\"\r\n" );
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document.write( "Use this principle on the left:\"+log%28B%2C%28A%29%29+-+log%28B%2C%28C%29%29+=+log%28B%2C%28A%2FC%29%29\"\r\n" );
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document.write( "\"log%283%2C%28%28%285x%2B5%29%29%2F%28%28x%5E2-1%29%29%29%29=0\"\r\n" );
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document.write( "Factor the numerator and denominator:\r\n" );
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document.write( "\"log%283%2C%28%285%28x%2B1%29%29%2F%28%28x-1%29%28x%2B1%29%29%29%29=0\"\r\n" );
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document.write( "Cancel the \"%28x%2B1%29\"'s\r\n" );
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document.write( "\"log%283%2C%28%285cross%28%28x%2B1%29%29%29%2F%28%28x-1%29cross%28%28x%2B1%29%29%29%29%29=0\"\r\n" );
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document.write( "\"log%283%2C%285%2F%28x%2B1%29%29%29=0\"\r\n" );
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document.write( "The log equation \"log%28B%2CA%29=C\" can be rewritten \r\n" );
document.write( "as the exponential equation \"A=B%5EC\"\r\n" );
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document.write( "\"5%2F%28x-1%29=3%5E0\"\r\n" );
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document.write( "Any number, except 0, raised to the 0 power is 1. So\r\n" );
document.write( "we replace \"3%5E0\" by \"1\"\r\n" );
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document.write( "\"5%2F%28x-1%29=1\"\r\n" );
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document.write( "Multiply both side by \"%28x-1%29\"\r\n" );
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document.write( "\"%28x-1%29\"\"5%2F%28x-1%29=%28x-1%291\"\r\n" );
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document.write( "\"cross%28%28x-1%29%29\"\"5%2Fcross%28%28x-1%29%29=%28x-1%291\"\r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "\"5=x-1\"\r\n" );
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document.write( "\"6=x\"\r\n" );
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document.write( "Edwin
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