How to substitute log_(10) for ln function?

Kolten Conrad 2022-07-15 Answered
How to substitute log 10 for ln function?
Im wondering how I could go about substituting log 10 for ln in the following formula?
y = a + b ln ( x + c )
Is there a simple way of doing this?
Cheers
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Answers (2)

Keegan Barry
Answered 2022-07-16 Author has 18 answers
Hint:
For any 1 a , b > 0
log a x = log b x log b a

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auto23652im
Answered 2022-07-17 Author has 5 answers
There is a a formula to change from base k to base b. See log b x = log k x log k b .
In your equation you have log ( x + c ) ( log is the natural logarithm). If we apply the change of base rule we get:
log ( x + c ) = log 10 ( x + c ) log 10 e ,
where e = exp ( 1 ) is the exponetial of 1 e = 2.71828
Therefore your equation is simply:
y = a + b log 10 e log 10 ( x + c ) ,

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