document.write( "Question 313421: if a^2+b^2=7ab,prove that log 1/3(a+b)=1/2[log a+log b] \n" ); document.write( "
Algebra.Com's Answer #224097 by CharlesG2(834)\"\" \"About 
You can put this solution on YOUR website!
if a^2+b^2=7ab,prove that log 1/3(a+b)=1/2[log a+log b]\r
\n" ); document.write( "\n" ); document.write( "log rule: logb (mn) = logb (m) + logb (n)
\n" ); document.write( "log rule: logb (m^n) = nlogb (m)\r
\n" ); document.write( "\n" ); document.write( "log [(1/3)(a + b)] = (1/2)(log a + log b)
\n" ); document.write( "log [(1/3)(a + b)] = (1/2)(log ab)
\n" ); document.write( "2log [(1/3)(a + b)] = log ab (multiplied both sides by 2)
\n" ); document.write( "log [(1/3)^2 * (a + b)^2] = log ab
\n" ); document.write( "log [(1/9)(a + b)^2] = log ab
\n" ); document.write( "(1/9)(a + b)^2 = ab (removed the logs)
\n" ); document.write( "(7/9)(a + b)^2 = 7ab (multiplied both sides by 7)
\n" ); document.write( "(7/9)(a^2 + 2ab + b^2) = 7ab (multiplied the left side out using FOIL)
\n" ); document.write( "and a^2+b^2 = 7ab (this is supposed to be true)
\n" ); document.write( "a^2 + b^2 = (7/9)(a^2 + 2ab + b^2) (set them equal)
\n" ); document.write( "9a^2 + 9b^2 = 7a^2 + 14ab + 7b^2 (multiplied both sides by 9)
\n" ); document.write( "2a^2 + 2b^2 = 14ab (subtracted 7a^2 + 7b^2 from both sides)
\n" ); document.write( "a^2 + b^2 = 7ab (divided both sides by 2)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );