If ∫log10x dx=K.xlogf(x)+c, then K,f(x)=

Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

If $\int \log_{10} x d x = K . x \log f (x) + c,$ then $K, f (x) =$

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

$\log_{e} 10, \frac{x}{e}$

$\log_{10} e, \frac{e}{x}$

$\log_{2} 10, \frac{x}{e}$

$\log_{10} e, \frac{x}{e}$

answer is D.

(Unlock A.I Detailed Solution for FREE)

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

$I = \int \log_{10} x d x$

$= \log_{10} e \int \log_{e} x d x$

$= \log_{10} e [x \log x - \int x . \frac{1}{x} d x] + c$

$= \log_{10} e [x \log x - x] + c$

$= \log_{10} e . x \log (\frac{x}{e}) + c$

$∴ K = \log_{10} e, f (x) = \frac{x}{e}$

Watch 3-min video & get full concept clarity

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test