Functions > Trigonometric, Log, and Exponential > Exponential and Logarithmic Functions
Exponential and Logarithmic Functions
exp(z)—Returns the number e raised to the power z.
log(z, [b])—Returns the base b logarithm of z. If b is omitted, returns base 10 log of z.
ln(z)—Returns the natural logarithm (base e) of z.
ln0(z)—Returns the natural logarithm (base e) of z, but returns –1×10307 at z = 0.
z is a dimensionless scalar (real, complex, or imaginary), or a vector of scalars.
For functions log and ln, z cannot be zero. If z is a vector, then none of its elements can be a zero.
b (optional) is a positive real scalar or scalar vector. If omitted, b is assumed to be 10.
If b is a vector, then none of its elements can be a zero and it must have the same length as vector z.
For complex z, the log functions return values from the principal branch of these functions, or ln(z) = ln(|z|) + i arg(z)
The exp function is equivalent to raising e to a power, but these both use a different algorithm than standard exponentiation. For very large or small values in the exponent, this algorithm is more robust, avoiding numerical roundoff errors. The most accurate values for very large arguments can be found using symbolic evaluation of exp(x) with a decimal argument:
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