Question

Evaluate:
log6 (1/36)
Please help me understand.

Answer 1

\[\log_{6} (1/36)\]

Answer 2

hint 36=6^2

Answer 3

use the division property for logs

Answer 4

I have almost zero understnading you'll have to walk me through it. My math lesson din't really help.

Answer 5

\[\log_a(\frac{n}{m})=\log_a(n)-\log_a(m) \\ \log_a(1)=0 \\ \log_a(a)=1 \\ \log_a(x^r)=r \log_a(x)\]

Answer 6

i would use all of these properties

Answer 7

it is like a puzzle

Answer 8

try to see if you can fit these together somehow to get an answer

Answer 9

For evaluating should i get a single number or should I still end up with an equation?

Answer 10

I have NO idea

Answer 11

Well you don't have an equation to start out with...
You have a expression so you will end up with an expression.
It will be a more simplified expression.

Answer 12

do you know how to use the first property I mentioned?

Answer 13

No, I need a walk through

Answer 14

None of it makes sense

Answer 15

\[\log_a(\frac{n}{m})=\log_a(n)-\log_a(m) \\ \text{ and you have } \\ \log_6(\frac{1}{36})\]
so it looks like n is 1 and m is 36 and a is 6
I bet you can plug in those numbers.

Answer 16

\[\log_{6}(1) - \log_{6}(36) \]

Answer 17

right

Answer 18

\[\log_a(\frac{n}{m})=\log_a(n)-\log_a(m) \\ \log_a(1)=0 \\ \log_a(a)=1 \\ \log_a(x^r)=r \log_a(x) \]
now looking at these equations here
which one can be applied to the log(1) thing?

Answer 19

The second one. So it is 0 now?

Answer 20

so then we just have to look at \[-\log_6(36)\]

Answer 21

and the hint I gave is that 36 can be written as 6^2

Answer 22

that 2 is a power
which equation has a power involved from my list

Answer 23

the last one

Answer 24

\[- \log _6(6^2)=-(2)\log_6(6)\]
so you see the power can be brought down from the last one

Answer 25

Yup.

Answer 26

now you have one more property to use and you are done

Answer 27

look at the list one more time

Answer 28

The log6(6)= 1

Answer 29

So the answer is -2?

Answer 30

\[\log_6(\frac{1}{36}) \\ \log_6(1)-\log_6(36) \\ 0-\log_6(36) \\ -\log_6(36) \\ -\log_6(6^2) \text{ since } 36=6^2 \\ -(2)\log_6(6) \\ -2(1) \\ -2 \\ \text{ and yes }\]

Answer 31

yes

Answer 32

Thanks so much! That made sense. :D