document.write( "Question 560326: Solve the equation 7^(x – 2) = 5^x. Round the answer to four decimal places. Thanks. :) \n" ); document.write( "
Algebra.Com's Answer #363835 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "7x - 2 = 5x\r\n" );
document.write( "\r\n" );
document.write( "Take logarithms of both sides:\r\n" );
document.write( "\r\n" );
document.write( "log(7x - 2) = log(5x)\r\n" );
document.write( "\r\n" );
document.write( "Use a rule of lagarithms that allows an exponent to come \r\n" );
document.write( "out in front as a multiplier\r\n" );
document.write( "\r\n" );
document.write( "(x - 2)log(7) = x·log(5)\r\n" );
document.write( "\r\n" );
document.write( "To make the algebra less bulky and cumbersome, \r\n" );
document.write( "let A = log(7) and B = log(5), then we have\r\n" );
document.write( "\r\n" );
document.write( "(x - 2)A = x·B\r\n" );
document.write( "\r\n" );
document.write( "A(x - 2) = Bx\r\n" );
document.write( "\r\n" );
document.write( "Ax - 2A = Bx\r\n" );
document.write( "\r\n" );
document.write( "Get both x terms on the left side \r\n" );
document.write( "and the non-x term on the right side:\r\n" );
document.write( "\r\n" );
document.write( "Ax - Bx = 2A\r\n" );
document.write( "\r\n" );
document.write( "Factor out x\r\n" );
document.write( "\r\n" );
document.write( "x(A - B) = 2A\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by (A - B)\r\n" );
document.write( "\r\n" );
document.write( "\"%28x%28A-B%29%29%2F%28A-B%29\" = \"%282A%29%2F%28A-B%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28x%28cross%28A-B%29%29%29%2F%28cross%28A-B%29%29\" = \"2A%2F%28A-B%29\"\r\n" );
document.write( "\r\n" );
document.write( "x = \"2A%2F%28A-B%29\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute log(7) for A and log(5) for B\r\n" );
document.write( "\r\n" );
document.write( "x = \"%282log%287%29%29%2F%28log%287%29-log%285%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "x = 11.56654212 round to 11.5665\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );