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

stylaria3y

Answered question

2022-07-21

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?

Answer & Explanation

Bradley Sherman

Bradley Sherman

Beginner2022-07-22Added 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
Makenna Booker

Makenna Booker

Beginner2022-07-23Added 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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