Question

2log6+log (1/3)=log12
which properties of logarithmics are/is used?

power property and product property
quotient property and product property
quotient property only
power property only

Answer 1

Well If I asked you what 2log6 + log(1/3) was, how would you solve it (without using a calculator)?

Answer 2

my teacher didnt go over this but still put it on the end of course exam

Answer 3

log (1/3) is saying -log 3. With that we can use quotient property

Answer 4

If it's just 2log6 +log(1/3) you can reduce it down to 2log6-log(3) because log(1) equal zero

Answer 5

2log6 can be written as log6^2
so, log 36

Answer 6

log36/log 3 is log 12

Answer 7

No it's not. log36 - log3 is log12.

Answer 8

same thing

Answer 9

make sense?

Answer 10

no it isn't.

\[\frac{log\ 36}{log\ 3} \ne log(\frac{36}{3})\]

Answer 11

log36-log3 =log36/log3

Answer 12

i'm not saying log(36/3)

Answer 13

No, it doesn't.

log 36 - log 3 = log(36/3)

Answer 14

>>> log(36, 10) - log(3, 10)
1.0791812460476247
>>> log(36,10)/log(3,10)
3.2618595071429146

Answer 15

Very different numbers.

Answer 16

try it in your calculator, (or wolframalpha)

Answer 17

log(36/3) is log(12) i checked with calculator and got the same answer so sorry for confusion just disregard the log36/log3

Answer 18

You can see quite trivially that it will be equal because 36/3 is 12. So log of 36/3 would be the log of 12. The problem is more about finding that log(36) - log(3) can be written as log(36/3)

Answer 19

ok so what was the problem?

Answer 20

The problem with your answer was that you said log(36) - log(3) = log(36)/log(3).

But the simplest solution is to just say:
\[2log6+log (1/3)\]
\[=log36 + log(\frac{1}{3})\]
\[=log (36 \times \frac{1}{3})\]
\[=log(12)\]

Which just uses the power and product rules. That said though you could also solve it by just using the product rule, or using the quotient rule and the power rule. So there's no non-ambiguous way to answer the multiple choice.