Question

★ CONTENT QUALITY SUPPORT REQUIRED ★

★ STANDARD QUESTION 66 ★

The answer with highest efficiency will get marked THE Brainliest , And will be offered an special invitation card

Question is -

If f(x) = logx ,
Then evaluate ,
$\frac{f(xy) + f \frac{x}{y} }{f(x)f(y)}$



This question needs a perfect answer ; and it doesn't support lazy ones ! Take care

Answer 1

f(xy)= log(xy) = log x + logy
log(x)(y) = f(x)(y)
logx logy = f(x)f(y)
then
logx +log y + log(x y)/( log x)(log y)
1/ logy + 1/log x + 1/ logy + 1/logx
2 (1/log x + 1 / log y)
Hope it helps!!

Answer 2

f(x)=log x
f(xy)=log(xy)=log x+log y..(I)
f(x/y)=log (x/y)=log x-log y..(ii)
=>[f(xy)+f(x/y)][f(x)*f(y)
=(log x+log y+log x-log y)/log(x)log(y)
=2log x/logx log y=2/log y