properties of logarithms ln12-ln2=ln6 I checked wolframalpha and it says that ln12-ln2=ln6. How? i tried to do: ln12=ln(2*2*3) which may be 2ln(2*3) (which is probably wrong). I need help. EDIT: Ok, thanks. Actually i could have just searched logarithms properties on google(didn't think about it). Sorry for taking your time.

Bridger Holden 2022-09-06 Answered
properties of logarithms ln 12 ln 2 = ln 6
I checked wolframalpha and it says that ln12-ln2=ln6. How? i tried to do: ln12=ln(2*2*3) which may be 2ln(2*3) (which is probably wrong). I need help.
EDIT: Ok, thanks. Actually i could have just searched logarithms properties on google(didn't think about it). Sorry for taking your time.
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Answers (2)

Krha77
Answered 2022-09-07 Author has 8 answers
You need to remember that
ln a ln b = ln ( a b )
Applying that here gives you
ln ( 12 ) ln ( 2 ) = ln ( 12 2 ) = ln ( 6 )
Note, alternatively, that we can use the property
ln ( a b ) = ln a + ln b
as well.
ln ( 12 ) = ln ( 2 6 ) = ln ( 2 ) + ln 6
So
ln ( 12 ) ln 2 = ln 2 + ln 6 ln 2 = ln 6
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Sonia Rowland
Answered 2022-09-08 Author has 1 answers
Hint: Use the property
ln x ln y = ln x y .
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