document.write( "Question 478711: Hi,\r
\n" ); document.write( "\n" ); document.write( "I tried to solve 5^logx=50-x^log5 in the following manner
\n" ); document.write( "Re- aligning the equation
\n" ); document.write( "5^logx+x^log5 =50
\n" ); document.write( "Taking log both sides
\n" ); document.write( "logx X log5 + logx X log5=log50
\n" ); document.write( "log(x+5) + log(x+5)=log50
\n" ); document.write( "From here am having confusion
\n" ); document.write( "1.
\n" ); document.write( "log(x+5)(x+5)=log50
\n" ); document.write( "log(x+5)^2=log50
\n" ); document.write( "(x+5)^2=50=>x=(50)^1/2-(5) (or)
\n" ); document.write( "2.
\n" ); document.write( "log(x+5) + log(x+5)=log50
\n" ); document.write( "2log(x+5)=log50
\n" ); document.write( "2(x+5)=50
\n" ); document.write( "x+5=25
\n" ); document.write( "x=20\r
\n" ); document.write( "\n" ); document.write( "Which is correct?\r
\n" ); document.write( "\n" ); document.write( "Thanks and regards,
\n" ); document.write( "AN
\n" ); document.write( "

Algebra.Com's Answer #327998 by Tatiana_Stebko(1539)\"\" \"About 
You can put this solution on YOUR website!
I am sorry, but all incorrect
\n" ); document.write( "Your error - you incorrect use formula \"log%28c%2Ca%29%2Blog%28c%2Cb%29=log%28c%2C+%28ab%29%29\"
\n" ); document.write( "\"5%5Elogx=50-x%5Elog5\"
\n" ); document.write( "Let \"t=5%5Elogx\"
\n" ); document.write( "then \"logt=log%28%285%5Elogx%29%29\" Formula \"log%28c%2Ca%5En%29=n%2Alog%28c%2Ca%29\", so
\n" ); document.write( "\"logt=logx%2Alog5\" or \"logt=log5%2Alogx\" we can write it in this way \"logt=log%28%28x%5Elog5%29%29\", then \"t=x%5Elog5\"
\n" ); document.write( "So \"5%5Elogx=x%5Elog5\"
\n" ); document.write( "Substitute in equation
\n" ); document.write( "\"5%5Elogx=50-5%5Elogx\"
\n" ); document.write( "\"5%5Elogx%2B5%5Elogx=50\"
\n" ); document.write( "\"2%2A5%5Elogx=50\"
\n" ); document.write( "\"5%5Elogx=50%2F2\"
\n" ); document.write( "\"5%5Elogx=25\"
\n" ); document.write( "\"5%5Elogx=5%5E2\"
\n" ); document.write( "\"logx=2\"
\n" ); document.write( "\"x=10%5E2\"
\n" ); document.write( "\"x=100\"
\n" ); document.write( "
\n" );