document.write( "Question 74624This question is from textbook Algebra and Trignometry
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\n" ); document.write( "\n" ); document.write( "(2^x)-(3^x)=0\r
\n" ); document.write( "\n" ); document.write( "I tried to bring it to base 2 but it didn't work. Please show us steps. \r
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Algebra.Com's Answer #53599 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!
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document.write( ": Solve: \r\n" );
document.write( "(2^x)-(3^x)=0 \r\n" );
document.write( "I tried to bring it to base 2 but it didn't work. Please show us steps. \r\n" );
document.write( "Thank you. \r\n" );
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document.write( "2x - 3x = 0\r\n" );
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document.write( "     2x = 3x\r\n" );
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document.write( "There are two log bases on your\r\n" );
document.write( "calculator, \"log\" which is the \r\n" );
document.write( "logarithm base 10, and \"ln\" which\r\n" );
document.write( "is the natural logarithm base \"e\".\r\n" );
document.write( "You can use either one:\r\n" );
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document.write( "If we use \"log\", we take the log     |    If we use \"ln\", we take the ln\r\n" );
document.write( "of both sides:                       |    of both sides:\r\n" );
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document.write( "  log(2x) = log(3x)                          ln(2x) = ln(3x)\r\n" );
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document.write( "Now we use the rule of logs to       |    Now we use the rule of lns to\r\n" );
document.write( "rewrite both sides:                  |   rewrite both sides:\r\n" );
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document.write( "  log(AB) = B·log(A)                        ln(AB) = B·ln(A)\r\n" );
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document.write( " x·log(2) = x·log(3)                 |     x·ln(2) = x·ln(3)\r\n" );
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document.write( "Get 0 on the right                   |   Get 0 on the right\r\n" );
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document.write( " x·log(2) - x·log(3) = 0             |    x·ln(2) - x·ln(3) = 0\r\n" );
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document.write( "Factor out x on the left:            |   Factor out x on the left:     \r\n" );
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document.write( " x·[log(2) - log(3)] = 0             |    x·[ln(2) - ln(3)] = 0\r\n" );
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document.write( "Using the calculator:                |   Using the calculator:\r\n" );
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document.write( "     x·{.301 - .477) = 0             |    x·(.693 - 1.099) = 0\r\n" );
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document.write( "           x·(-.176) = 0             |           x·(-.406) = 0\r\n" );
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document.write( "              -.176x = 0             |              -.406x = 0\r\n" );
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document.write( "Divide both sides by -.176           |  Divide both sides by -.406\r\n" );
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document.write( "                   x = 0             |                   x = 0\r\n" );
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document.write( "                    Either way you get x = 0 \r\n" );
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document.write( "Checking:\r\n" );
document.write( "             2x - 3x = 0\r\n" );
document.write( "             20 - 30 = 0\r\n" );
document.write( "               1 - 1 = 0\r\n" );
document.write( "                   0 = 0\r\n" );
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document.write( "Edwin
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