Question

LOG

Answer 1

Which of the statements are true
(A)\[\log_23<\log_{12}10\]
(B)\[\log_65<\log_78\]
(C)\[\log_326<\log_29\]
(D)\[\log_{16}15>\log_{10}11>\log_76\]

I am able to do this but my method takes 3 pages for ebery option, So i want a smart way

Answer 2

Every****

Answer 3

http://www.1728.org/logrithm.htm

Answer 4

\(\Large \log_ab=c \implies b=a
^c\)

log_2 3 = x

2^x = 3
x is surely greater than 1

log_12 10 = y
12^y = 10

y is surely less than 1

Answer 5

same can be applied to (B) and (C)

Answer 6

@SolomonZelman calc is not allowed

Answer 7

me read you method hartn

Answer 8

for (C), x<3, y>3

Answer 9

Wait let me read you method

Answer 10

we can do this by inspection


so notice that on the left side
the base is smaller which is 2 but in the right
the base is larger now before we proceed. let me first ask you
lets say we have :