document.write( "Question 1072415: Solve for x in each:
\n" ); document.write( "A) 9^(2x+3) =81^(2x-1)\r
\n" ); document.write( "\n" ); document.write( "B)2log2x=log(7x-3)
\n" ); document.write( "C)7*3^(x+2)=5x
\n" ); document.write( "d)log3(x+1)+log3(x+6)=2
\n" ); document.write( "E) log10^e \n" ); document.write( "
Algebra.Com's Answer #687332 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
A) 9^(2x+3) =81^(2x-1)
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document.write( "Write 81 as 92\r\n" );
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document.write( "\"9%5E%282x%2B3%29=%289%5E2%29%5E%282x-1%29\"\r\n" );
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document.write( "Multiply the exponents on the right\r\n" );
document.write( "to rmove the parentheses:\r\n" );
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document.write( "\"9%5E%282x%2B3%29=9%5E%282%282x-1%29%29\"\r\n" );
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document.write( "Since the exponents on each side have\r\n" );
document.write( "the same positive base other than 1,\r\n" );
document.write( "The exponents are equal, so\r\n" );
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document.write( "\"2x%2B3=2%282x-1%29\"\r\n" );
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document.write( "You finish.\r\n" );
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\n" ); document.write( "B)2log(2x)=log(7x-3)
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document.write( "\"2%2Alog%28%282x%29%29=log%28%287x-3%29%29\"\r\n" );
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document.write( "Use the rule of logarithms that allows us\r\n" );
document.write( "to move the 2 coefficent on the left up\r\n" );
document.write( "above the (2x) as an exponent:\r\n" );
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document.write( "\"log%28%282x%29%5E2%29=log%28%287x-3%29%29\"\r\n" );
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document.write( "Now what the log is of on the left must be\r\n" );
document.write( "equal to what the log is of on the right,\r\n" );
document.write( "so\r\n" );
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document.write( "\"%282x%29%5E2=7x-3\"\r\n" );
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document.write( "You finish that.  It's a quadratic. \r\n" );
document.write( "Check both answers\r\n" );
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\n" ); document.write( "C)7*3^(x+2)=5x
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document.write( "There is no way to solve an equation if the variable\r\n" );
document.write( "appears both as part of exponent and also part of\r\n" );
document.write( "a non-exponent, except as an approximation using a\r\n" );
document.write( "graphing calculator.  However we can show with a\r\n" );
document.write( "calculator that it has no solution because the left\r\n" );
document.write( "side is always greater than the right side.\r\n" );
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\n" ); document.write( "d)log3(x+1)+log3(x+6)=2
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document.write( "I can't tell whether the 3's are bases of the logarithms\r\n" );
document.write( "or coefficients of the expressions in parentheses.\r\n" );
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\n" ); document.write( "E) log10^e
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document.write( "\"log\" with no base written means that the base is 10.  So\r\n" );
document.write( "\"log%2810%2C%2810%5Ee%29%29\" asks \"What exponent of the base is\r\n" );
document.write( "required to give what the log is of?\"  What the log is of\r\n" );
document.write( "is 10e, and so the exponent of the base 10 that\r\n" );
document.write( "is required to give what the log is of, namely 10e is\r\n" );
document.write( "simply the exponent e.\r\n" );
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document.write( "Edwin
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