document.write( "Question 922509: 4^(1-x)=3^(2x-5) \n" ); document.write( "
Algebra.Com's Answer #559607 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "\"4%5E%281-x%29=3%5E%282x-5%29\"\r\n" );
document.write( "\r\n" );
document.write( "We take the log of both sides:\r\n" );
document.write( "\r\n" );
document.write( "\"log%284%5E%281-x%29%29=log%283%5E%282x-5%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "There is a rule of logarithms that allows us to move an exponent\r\n" );
document.write( "in front as a multiplier of the log:\r\n" );
document.write( "\r\n" );
document.write( "\"%281-x%29log%284%29=%282x-5%29log%283%29\"\r\n" );
document.write( "\r\n" );
document.write( "To make things easier let log(4)=A and log(3)=B\r\n" );
document.write( "\r\n" );
document.write( "\"%281-x%29A=%282x-5%29B\"\r\n" );
document.write( "\r\n" );
document.write( "\"A%281-x%29=B%282x-5%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"A-Ax=2Bx-5B\"\r\n" );
document.write( "\r\n" );
document.write( "\"A%2B5B=2Bx%2BAx\"\r\n" );
document.write( "\r\n" );
document.write( "\"A%2B5B=%282B%2BA%29x\"\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides of the equation by (2B+A)\r\n" );
document.write( "\r\n" );
document.write( "\"%28A%2B5B%29%2F%282B%2BA%29=x\"\r\n" );
document.write( "\r\n" );
document.write( "Now replace A and B by the logs they represent:\r\n" );
document.write( "\r\n" );
document.write( "\"%28log%284%29%2B5%2Alog%283%29%29%2F%282%2Alog%283%29%2Blog4%29=x\"\r\n" );
document.write( "\r\n" );
document.write( "With a calculator we get\r\n" );
document.write( "\r\n" );
document.write( "1.919720789 = x\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );