document.write( "Question 970600: find x if x^log a base 2 + a^log x base 2 = 2a^2 (a>0) \n" ); document.write( "

Algebra.Com's Answer #594048 by anand429(138) $\"\"$ $\"About$

You can put this solution on YOUR website!
Given,
\n" ); document.write( " $\"x%5E%28log%282%2Ca%29%29%2Ba%5E%28log%282%2Cx%29%29=2a%5E2\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "=> x^(log(x,a)/log(x,2))+ $\"a%5E%28log%282%2Cx%29%29=2a%5E2\"$ (using $\"%28log%28a%2Cb%29%29=%28%28log%28x%2Cb%29%29%2F%28log%28x%2Ca%29%29%29\"$
\n" ); document.write( ".
\n" ); document.write( "=> a^(1/(log(x,2)))+ $\"a%5E%28log%282%2Cx%29%29=2a%5E2\"$
\n" ); document.write( "=> $\"a%5E%28log%282%2Cx%29%29%2Ba%5E%28log%282%2Cx%29%29=2a%5E2\"$
\n" ); document.write( "=> $\"2a%5E%28log%282%2Cx%29%29=2a%5E2\"$
\n" ); document.write( "Comparing exponents, we get,
\n" ); document.write( " $\"%28log%282%2Cx%29%29=2\"$
\n" ); document.write( "=> $\"x=2%5E2\"$
\n" ); document.write( "=> $\"x=4\"$ \n" ); document.write( "

\n" );