# Logarithm and exponential in R

Logarithms and exponential can be computed making use of the functions provided by R: the `log`

function for natural logarithms, `log2`

and `log10`

for base 2 and 10 logarithms, respectively, `log1p`

to compute `log(1 + x)`

and the `exp`

function to compute the exponential function and `expm1`

to calculate `exp(x) - 1`

.

## log()

The basic R function to compute logarithms is `log`

, which **calculates natural logarithms**. The syntax of the function is as follows.

`log(x, base = exp(1))`

Note that the `base`

argument allows you to customize the base of the logarithm. In the following block of code you can see some examples.

```
log(8)
log(0)
log(1)
log(10)
log(12, base = 2)
```

```
2.079442
-Inf
0
2.302585
3.584963
```

You can make use of the plot function to represent the values of a natural logarithm:

```
plot(log, 0, 100, col = 4, main = "log(x)")
segments(x0 = exp(1), y0 = 0, x1 = exp(1), y1 = 1, lty = 2)
segments(x0 = 0, y0 = 1, x1 = exp(1), y1 = 1, lty = 2)
points(exp(1), 1, pch = 16)
```

## log2()

The `log2`

function calculates a **logarithm with base 2** and is equivalent to `log(x, base = 2)`

.

```
log2(10)
log(10, base = 2) # Equivalent
```

```
3.321928
3.321928
```

You can see a visual representation of the logarithm of base 2 from 0 to 100 in the following chart:

```
plot(log2, 0, 100, col = 4, main = "log2(x)")
segments(x0 = 2, y0 = 0, x1 = 2, y1 = 1, lty = 2)
segments(x0 = 0, y0 = 1, x1 = 2, y1 = 1, lty = 2)
points(2, 1, pch = 16)
```

## log10()

The `log10`

function is a wrapper of `log(x, base = 10)`

and computes a **logarithm of base 10**.

```
log10(10)
log(10, base = 10) # Equivalent
```

```
1
1
```

You can plot this function with the following block of code:

```
plot(log10, 0, 100, col = 4, main = "log10(x)")
segments(x0 = 10, y0 = 0, x1 = 10, y1 = 1, lty = 2)
segments(x0 = 0, y0 = 1, x1 = 10, y1 = 1, lty = 2)
points(10, 1, pch = 16)
```

## log1p()

The `log1p()`

function computes `log(1 + x)`

, accurately also for `|x| âȘ 1`

.

```
# log(10)
log(10)
# log(1 + 10)
log1p(10)
# log(11)
log(11)
```

```
2.302585
2.397895
2.397895
```

You can plot this function with the following line of code:

`plot(log1p, -0.99, 10, col = 4, main = "log1p(x)")`

## exp()

The `exp`

function in R **computes the exponential function**, which is the inverse of the natural logarithm. The following block contains some examples of the usage of the `exp`

function.

```
exp(10)
exp(0)
exp(-5)
exp(4)
```

```
22026.47
1
0.006737947
54.59815
```

You can also plot the exponential function making use of the `plot`

function as shown below:

`plot(exp, -10, 10, col = 4, main = "exp(x)")`

## expm1()

The `expm1`

function computes `exp(x) -1`

, accurately also for `|x| âȘ 1`

.

```
expm1(5)
exp(5) - 1
expm1(0.15)
exp(0.15) - 1
```

```
147.4132
147.4132
0.1618342
0.1618342
```

You can use the following line of code to plot this function for different values.

`plot(expm1, -10, 10, col = 4, main = "expm1(x)")`