\n" ); document.write( "please show me how to work this out because I am stuck\r
\n" ); document.write( "\n" ); document.write( "also the exponent for 3 is 2x
\n" ); document.write( "the exponent for 2 is x-1
Algebra.Com's Answer #648322 by Theo(13342)![\"\"](\"/images/stars/stars-13.gif\")  You can put this solution on YOUR website! \n" ); document.write( "your equation is 3^(2x) = 2^(x-1) \n" ); document.write( "take the log of both sides of the equation to get: \n" ); document.write( "log(3^(2x)) = log(2^(x-1)) \n" ); document.write( "since log(a^b) = b*log(a), your expression becomes: \n" ); document.write( "2x * log(3) = (x-1) * log(2) \n" ); document.write( "simplify to get 2x * log(3) = x * log(2) - log(2) \n" ); document.write( "subtract x * log(2) from both sides of the equation to get: \n" ); document.write( "2x * log(3) - x * log(2) = - log(2) \n" ); document.write( "factor out the x on the left side of the equation to get: \n" ); document.write( "x * (2 * log(3) - log(2)) = - log(2) \n" ); document.write( "divide both sides of this equation by (2 * log(3) - log(2)) to get: \n" ); document.write( "x = - log(2) / (2 * log(3) - log(2)) \n" ); document.write( "simplify to get: \n" ); document.write( "x = - .4608454206 \n" ); document.write( "that should be your answer. \n" ); document.write( "replace x with that in the original equation of 3^(2x) = 2^(x-1) \n" ); document.write( "you will get .3632801844 = .3632801844 \n" ); document.write( "that confirms the solution is correct.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |