document.write( "Question 136498: Hi. I've been trying to solve this for about three hours. I know the solution is 11.0834645967, but I can't figure out how to get it within the constraints of the problem: Show how to solve the following equation in terns of the common logarithm. Also give an approximation of the solution to the nearest hundreth of a unit. 3^(2x-3)=5^(x+2)\r
\n" ); document.write( "\n" ); document.write( "My work is
\n" ); document.write( "log(3^2x-3)=log(5^x+2)\r
\n" ); document.write( "\n" ); document.write( "(2x-3)log3=(x+2)log5\r
\n" ); document.write( "\n" ); document.write( "2x-3=(x+2)log5/log3\r
\n" ); document.write( "\n" ); document.write( "(2x-3)/(x+2)=log5/log3\r
\n" ); document.write( "\n" ); document.write( "(2x-3)/(x+2)=logbase3 5\r
\n" ); document.write( "\n" ); document.write( "and then I get stuck. And I might have gone right past the correct route and gotten more tangled. Any help would be most appreciated. \n" ); document.write( "

Algebra.Com's Answer #99993 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
Hi. I've been trying to solve this for about three hours. I know the solution is 11.0834645967, but I can't figure out how to get it within the constraints of the problem: Show how to solve the following equation in terns of the common logarithm. Also give an approximation of the solution to the nearest hundreth of a unit. \r
\n" ); document.write( "\n" ); document.write( " $\"3%5E%282x-3%29=5%5E%28x%2B2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "My work is \r
\n" ); document.write( "\n" ); document.write( " $\"++log%28%28++3%5E%282x-3%29+%29%29+=+log%28%28++5%5E%28x%2B2%29++%29%29++\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+%282x-3%29log%28%283%29%29+=+%28x%2B2%29log%28%285%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2x-3=%28x%2B2%29%28log%28%285%29%29%2Flog%28%283%29%29%29\"$
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document.write( "You did fine to here.  Then you went astray. Now here is what \r\n" );
document.write( "you should have done:\r\n" );
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document.write( "Get your calculator at this point and calculate  as\r\n" );
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document.write( "and store it in the memory of your calculator, or write it down.\r\n" );
document.write( "So you won't have to cary such a long awkward decimal through your\r\n" );
document.write( "steps, just call it .  In other words let \r\n" );
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document.write( "Now \r\n" );
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document.write( "becomes simply\r\n" );
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document.write( "or switch the A to the left of the parentheses:\r\n" );
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document.write( "Distribute on the right:\r\n" );
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document.write( "Get all the x terms on the left and other terms on the right:\r\n" );
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document.write( "Factor out x on the left:\r\n" );
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document.write( "Divide both sides by \r\n" );
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document.write( "Cancel the 's\r\n" );
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document.write( "Now using the recall feature of your calculator to substitute\r\n" );
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document.write( "Now calculate that with your calculator, and you'll get\r\n" );
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document.write( "Edwin

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