Change base log formula? y=a*ln⁡(x+c)+b The ln equation is: y=17.686797186426052 * ln(x + 0.3)

Iris Vaughn

Iris Vaughn

Answered question

2022-10-14

Change base log formula?
Im trying to change the base log from ln to log with the following formula.
y = a * ln⁡(x+c) + b
The ln equation is:
y = 17.686797186426052 * ln(x + 0.3) + -79.52230886298399
And considering that:
ln(X)=2.302585 log(X)
I was trying to change the equation to use log function (to this):
y = 17.686797186426052 * 2.302585 * log(x + 0.3) + -79.52230886298399
However, for some reason it's not working. Id be really grateful for some pointers on where I might be going wrong?
Cheers

Answer & Explanation

bigfreakystargl

bigfreakystargl

Beginner2022-10-15Added 23 answers

Rewrite the formula as
y = a ln ( x + c ) + b = a log e ( x + c ) + b = a log k ( x + c ) log k e + b = a log k e log k ( x + c ) + b .
If you want the logarithm in base- 10, then you simply write
y = a log e log ( x + c ) + b .
Now, you can plug in the values of a, b, and c without having trouble.

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