Question

how to simplify

Answer 1

\[\frac{\log_3{12}\times \log_4{12}}{\log_3{12}+\log_4{12}} \]

Answer 2

i can't understand this question which property will come into use :(

Answer 3

a very tilting question

Answer 4

\[\frac{\log_{3}12}{\log_{3}{12}+\log_4{12}}\times \log_4{12}\]

Answer 5

um if you put in calculator its 1.. or do i need to use differents bases to simplify by hand

Answer 6

wait lemme find a property to solve this question

Answer 7

@mathslover is there any property something like this\[\log_{a}{b}+\log_{c}{b}=\log_{ac}{b}\]????????

Answer 8

\[\log_a b \times \log_a c = \log_a (b\times c)\]change of base.

Answer 9

Ops! That's a positive in b/w on the left side.

Answer 10

\[\log_a b + \log_a c = \log_a(b\times c)\]

Answer 11

\[\large{\cfrac{\frac{1}{\log_{12}{3}}*\frac{1}{\log _{12}4}}{\frac{1}{\log_{12}3}+\frac{1}{log_{12}4}}}\]

Answer 12

always remember that:
\[\large{\log_ab=\frac{1}{\log_ba}}\]

Answer 13

can u solve further @powerangers69

@jiteshmeghwal9 dude this is the correct way

Answer 14

k!

Answer 15

sorry! i forgot the change of base

Answer 16

no problem ... we can further conclude and we will get the answer as 1

Answer 17

thanks!!

Answer 18

alternative

\( \frac{\ln 12/ \ln 3 * \ln 12/ \ln 4} {\ln 12/ \ln 3 + \ln 12 / \ln 4}\)

\( \frac{\ln 12 * \ln 12}{\ln 12 * \ln 4 + \ln 12 * \ln 3}\)

\( \frac{\ln 12 * \ln 12}{ \ln 12 ( \ln 4 + \ln 3) } \)

\(\frac{\ln 12}{(ln 4 + ln 3)}\)

Answer 19

welcome and best of luck