document.write( "Question 544494: how do you solve the following logarithmic equation $\"log%5E3%28x-2%29%2Blog%5E3%28x-8%29=3\"$ be sure to reject the domain and expressions \n" ); document.write( "

Algebra.Com's Answer #355985 by lwsshak3(11628) $\"\"$ $\"About$

You can put this solution on YOUR website!
log^3(x-2)+log^3(x-8)=3
\n" ); document.write( "log3[(x-2)(x-8)]=3
\n" ); document.write( "convert to exponential form: base(3) raised to log of number(3)=number[(x-2)(x-8)]
\n" ); document.write( "3^2=[(x-2)(x-8)]=9
\n" ); document.write( "x^2-10x+16=0
\n" ); document.write( "(x-8)(x-2)=0
\n" ); document.write( "x=8 (reject, (x-8)>0)
\n" ); document.write( "or
\n" ); document.write( "x=2 (reject, (x-8)>0)
\n" ); document.write( "Therefore, no solution \n" ); document.write( "

\n" );