Question

log12 (4) + 1/ 2log36 (2) + log36 (3)
evaluate the expression

Answer 1

\[\log_{12}(4)+\frac{ 1 }{ 2}\log_{36}(2) +\log_{36}(3)\]
Is this your expression?

Answer 2

no, 1 over (2log36 (2)+log 36 (3))

Answer 3

\[\log_{b^n}a^m=\frac{ m }{ n } \log_{b} a\]

Answer 4

@kY_Tan :What you think the first step should be?

Answer 5

log12 (4)+ 1/(log36 (4)+log36 (3))
log12 (4)+ 1/(log36 (12))

Answer 6

Where did we get a 4? \(\log(2) + log(3) = log(6)\)

Answer 7

@tkhunny: you missed the "2" before \[\log_{36} (2)\]

Answer 8

Ah, that makes more sense.

Answer 9

In proper terms;\[\log_{12}(4)+ \frac{1 }{ 2\log_{36} (2)+\log_{36} (3) }\]

Answer 10

So what should be the next step @kY_Tan ?

Answer 11

and then log12(4) +log36 (36)/log36 (12)?

Answer 12

i tried for it many times but can't get the correct answer

Answer 13

"log36 (36)/log36 (12)" is same 1/log36 (12), so you are not going anywhere.

Answer 14

can't log36 (36)/log36 (12) be divided?

Answer 15

We have "2" different bases, you need to make one of them have equal base to the other.

Answer 16

It is divided but you still have "2" different bases, one with "12" and one with "36"

Answer 17

so what i already done until now is correct?

Answer 18

change the base to "12" by \[\frac{ \log_{12}(12) }{ \log_{12}(36) }\]

Answer 19

so after changing the base to 12
1/(log12 (12)/log12 (36))?

Answer 20

\[\log_{12} (4)+\frac{ 1 }{ \frac{ \log_{12}(12) }{ \log_{12}(36) } }\]

Answer 21

But we know \[\log_{12} 12=1\]What would be the next step?

Answer 22

@ kY_Tan : yes, you are correct!

Answer 23

can log12 (4) + 1/(1/3)?? or just log12 (4) + log12 (36)?

Answer 24

Don't simplify individual log function which do not provide discrete result.

Answer 25

\[\log_{12} (4)+\log_{12} 36=\log_{12} (36*4)=\log_{12} (144)\]

Answer 26

and sure we know; \[12^x=144\], what would be "x"?

Answer 27

oh ok i got it
12^x=144
x=2

Answer 28

Perfect! :)

Answer 29

thanks for your guide

Answer 30

My pleasure :)