Question

I'm having a little bit of trouble with logs (Well, more specifically, rewriting logs in terms of others).

log 6 (10)=1.3
log 6 (7)=1.1
log6 (8)=1.2

Find log 6 (3/50)

Answer 1

the gimmick is to figure out how two write \(\frac{3}{50}\) in terms of \(10, 7,8\)

Answer 2

oh and i guess \(6\) since that is the base

Answer 3

one question is it asking this ? \[\log_{6} (3/5)\]

Answer 4

or is the 6 multiplies by the (3/5)

Answer 5

gimmick is to do this
write \(\frac{3}{50}=\frac{6}{100}=\frac{6}{10^2}\)

Answer 6

The first one you said. except it's log6 (3/50)

Answer 7

@satellite73: Alright :) What next?

Answer 8

and so
\[\log_6(\frac{3}{50})=\log_6(\frac{6}{10^2})\] now break it apart

Answer 9

you get
\[\log_6(\frac{6}{10^2})=\log_6(6)-\log_6(10^2)=\log_6(6)-2\log(10)\]

Answer 10

you have all the numbers you need, since you are told \(\log_6(10)=1.3\) ( a lie, but no matter) and \(\log_6(6)\) should be obvious

Answer 11

Ah, okay, got it!
I have one other question I don't get.

log8 (12) = 1.2
log8 (7) = 0.9
log8 (9) = 1.1

Find log8 (81/7)