IIT JEE , AIEEE Forum - Mathematics , Algebra

blackjack

prove that- log710>log1113

blackjack

comeon guys, reply fast...........

LAMPARD

log₇10 is same as log10/log7=1/log7.Here,log7 is less than 1.
log₁₁13 is same as log13/log11.Here,log11 is greater than 1 and so log13/log11 will be approximately near 1.1-1.3 whereas 1/log7 will be greater coz log7 itself is less than 1.

sandeepramesh

how can you affirm that approximation?

blackjack

thanks, i got it..........

LAMPARD

C'mon yaar,how much will be the difference between log 13 and log11??.It will be very less since 90 such numbers(log11,log12,..log99) lie between 1 and 2.So,obviously,there isnt going to be much difference between them.

sandeepramesh

but you need to prove it with calculations no? things may look obvious but calculations are a must

nadeemoidu

There is no obvious business. we r supposed to prove it . saying that it is obvious is not a proof.

suppose I want to prove that u r wrong , can i just say that u r obviously wrong?

hsbhatt

Since $\frac{10}{7} > \frac{13}{11}$

Hence we have $\log_7(\frac{10}{7}) > \log_7(\frac{13}{11}) > \log_{11}(\frac{13}{11})$

So, $\log_7(\frac{10}{7}) +1 > \log_{11}(\frac{13}{11}) + 1$

or $\log_7 10 > \log_{11} 13$

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