R: Using equation with natural logarithm in nls

Question

Good day,

I am struggling with R and natural logarithm (ln). Firstly, I cannot find a ln(x) function in R. I have noticed that log(x) is the same as ln(x) (when using ln(x) with a calculator).

In R:

log(5) = 1.609438

And with a calculator:

ln(5) = 1.609438
log(5) = 0.69897

I'm trying to fit an equation in R (this is exactly how I found in the literature of 3 references):

y = a + b(^x/₃₀₅) + c(^x/₃₀₅)² + d ln(³⁰⁵/_x) + f ln²(³⁰⁵/_x)

Is it correct to use the following syntax in R to use the equation?

y ~ a + b*(x/305) + c*((x/305)^2) + d*log(305/x) + f*(log(305/x))^2

The idea is to use this function with nls() in R. Thanks in advance!

Answer 1

In R, log is the natural logarithm. In calculators, log usually means base 10 logarithm. To achieve that in R you can use the log10 function.

log(5)
## [1] 1.609438
log10
## [1] 0.69897(5)

As for your formula, it seems correct, since log is the natural logarithm.

Answer 2

In addition I will point out that your model

y ~ a + b*(x/305) + c*((x/305)^2) + d*log(305/x) + f*(log(305/x))^2

is linear in the statistical sense of being linear in the coefficients; it doesn't need to be linear in x.

You don't need nls to fit this model, you could use lm().

But remember to look at the I() function to express terms like (x/305)^2.

ETA example:

aDF <- data.frame(x=abs(rnorm(100)), y=rnorm(100))
lm(y ~ 1 + I(x/305) + I((x/305)^2) + log(305/x) + I(log(305/x)^2), data=aDF)