What log rule was used to simply this expression? I'm unclear how the left side is equal to the right side. 365log(365)−365−305log(305)+305−60log(365)=305log((365)/(305))−60 I know log(a)−log(b)=log(a/b) but if you stick constants before each ln() then how do you apply the rule to get 305 as the constant on the right side of the equation?

stylaria3y 2022-07-21 Answered
What log rule was used to simply this expression?
I'm unclear how the left side is equal to the right side.
365 log ( 365 ) 365 305 log ( 305 ) + 305 60 log ( 365 ) = 305 log ( 365 305 ) 60
I know log ( a ) log ( b ) = log ( a / b ) but if you stick constants before each ln() then how do you apply the rule to get 305 as the constant on the right side of the equation?
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Answers (2)

Bradley Sherman
Answered 2022-07-22 Author has 17 answers
There are a couple of steps missing.
  365 log ( 365 ) 365 305 log ( 305 ) + 305 60 log ( 365 ) = [ 365 log ( 365 ) 60 log ( 365 ) ] + [ 365 + 305 ] 305 log ( 305 ) = 305 log ( 365 ) 60 305 log ( 305 ) = [ 305 log ( 365 ) 305 log ( 305 ) ] 60 = 305 [ log ( 365 ) log ( 305 ) ] 60 = 305 log ( 365 / 305 ) 60

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Makenna Booker
Answered 2022-07-23 Author has 3 answers
Collect the constants (-365 + 305 = -60), and the terms with l o g ( 365 )
365 log ( 365 ) 365 305 log ( 305 ) + 305 60 log ( 365 ) = 305 log ( 365 ) 305 log ( 305 ) 60
Now factor out 305, and use the identity you mentioned:
305 ( log ( 365 ) log ( 305 ) ) 60 = 305 log ( 365 / 305 ) 60

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