# Exponents and Logarithms

Exponential, logarithm, power, and root functions

In addition to common functions like `exp` and `log`, MATLAB® has several other related functions to allow flexible numerical calculations. The `expm1` and `log1p` functions compensate for numerical round-off errors in small arguments, while the `reallog`, `realpow`, and `realsqrt` functions restrict the range of these functions to real numbers. `nthroot` calculates roots of any order, while the specialized functions `pow2` and `nextpow2` calculate powers of two.

## Functions

 `exp` Exponential `expm1` Compute exp(x)-1 accurately for small values of x `log` Natural logarithm `log10` Common logarithm (base 10) `log1p` Compute log(1+x) accurately for small values of x `log2` Base 2 logarithm and floating-point number dissection `nextpow2` Exponent of next higher power of 2 `nthroot` Real nth root of real numbers `pow2` Base 2 power and scale floating-point numbers `reallog` Natural logarithm for nonnegative real arrays `realpow` Array power for real-only output `realsqrt` Square root for nonnegative real arrays `sqrt` Square root

## Topics

Powers and Exponentials

This topic shows how to compute matrix powers and exponentials using a variety of methods.

Graphical Comparison of Exponential Functions

This example shows an interesting graphical approach for discovering whether e^pi is greater than pi^e.