log(x) function computes natural logarithms (Ln) for a number or vector x by default. If the base is specified, log(x,b) computes logarithms with base b.
log10 computes common logarithms (Lg). log2 computes binary logarithms (Log2).

log(x, base = exp(1))

log() by default computes the natural logarithms (Ln, with base e):

>log(5) #ln5
[1] 1.609438
> log(13.27) #ln(13.27)
[1] 2.585506

The base=x parameter specifies the calculation of the logarithms with base x:

>log(9,base=3) #log39 = 2

>log10(5) #lg5

[1] 0.69897

>log2(5) #log25

[1] 2.321928

[1] 2

Let's try vector:

>x <- rep(1:12)
>x

[1] 1 2 3 4 5 6 7 8 9 10 11 12

>log(x)

[1] 0.0000000 0.6931472 1.0986123 1.3862944 1.6094379 1.7917595 1.9459101
[8] 2.0794415 2.1972246 2.3025851 2.3978953 2.4849066

>log(x,6)

[1] 0.0000000 0.3868528 0.6131472 0.7737056 0.8982444 1.0000000 1.0860331
[8] 1.1605584 1.2262944 1.2850972 1.3382908 1.3868528

Let's plot the log() function:

> x <- seq(0,100,by=0.1)
> plot(x,log(x),typ="l",col="blue")