document.write( "Question 391533: (3x)^(log3)-(5x)^(log5)=0
\n" ); document.write( "Solve for x \n" ); document.write( "
Algebra.Com's Answer #279462 by lwsshak3(11628)\"\" \"About 
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(3x)^(log3)-(5x)^(log5)=0
\n" ); document.write( "Solve for x\r
\n" ); document.write( "\n" ); document.write( "(log3)(log3x)-(log5)(log5x)=0
\n" ); document.write( "log3(log3+logx)-log5(log5+logx)=0
\n" ); document.write( "(log3)^2+(log3)(logx)-(log5)^2-(log5)(logx)=0
\n" ); document.write( "(log3)(logx)-(log5)(logx)=(log5)^2-(log3)^2 (difference of 2 squares)
\n" ); document.write( "logx(log3-log5)=(log5-log3)(log5+log3)
\n" ); document.write( "logx=(log5-log3)(log5+log3)/-(log5-log3)
\n" ); document.write( "logx=-(log5+log3)=-1.17609
\n" ); document.write( "x=10^-1.17609=.06667 (definition of a logarithm, the base raised to the logarithm of the number is equal to the number)
\n" ); document.write( "ans: x=.06667\r
\n" ); document.write( "\n" ); document.write( "Check: (3*.06667)^log3-(5*.06667)^log5 = 0
\n" ); document.write( " = .464-.464 = 0
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