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<a name="Exponents-and-Logarithms"></a>
<div class="header">
<p>
Next: <a href="Complex-Arithmetic.html#Complex-Arithmetic" accesskey="n" rel="next">Complex Arithmetic</a>, Up: <a href="Arithmetic.html#Arithmetic" accesskey="u" rel="up">Arithmetic</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Exponents-and-Logarithms-1"></a>
<h3 class="section">17.1 Exponents and Logarithms</h3>

<a name="XREFexp"></a><dl>
<dt><a name="index-exp"></a>: <em></em> <strong>exp</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute
<code>e^x</code>
for each element of <var>x</var>.
</p>
<p>To compute the matrix exponential, see <a href="Linear-Algebra.html#Linear-Algebra">Linear Algebra</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFlog">log</a>.
</p></dd></dl>


<a name="XREFexpm1"></a><dl>
<dt><a name="index-expm1"></a>: <em></em> <strong>expm1</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute
<code>exp (<var>x</var>) - 1</code>
accurately in the neighborhood of zero.
</p>
<p><strong>See also:</strong> <a href="#XREFexp">exp</a>.
</p></dd></dl>


<a name="XREFlog"></a><dl>
<dt><a name="index-log"></a>: <em></em> <strong>log</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute the natural logarithm,
<code>ln (<var>x</var>)</code>,
for each element of <var>x</var>.
</p>
<p>To compute the matrix logarithm, see <a href="Linear-Algebra.html#Linear-Algebra">Linear Algebra</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFexp">exp</a>, <a href="#XREFlog1p">log1p</a>, <a href="#XREFlog2">log2</a>, <a href="#XREFlog10">log10</a>, <a href="Special-Utility-Matrices.html#XREFlogspace">logspace</a>.
</p></dd></dl>


<a name="XREFreallog"></a><dl>
<dt><a name="index-reallog"></a>: <em></em> <strong>reallog</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return the real-valued natural logarithm of each element of <var>x</var>.
</p>
<p>If any element results in a complex return value <code>reallog</code> aborts and
issues an error.
</p>
<p><strong>See also:</strong> <a href="#XREFlog">log</a>, <a href="#XREFrealpow">realpow</a>, <a href="#XREFrealsqrt">realsqrt</a>.
</p></dd></dl>


<a name="XREFlog1p"></a><dl>
<dt><a name="index-log1p"></a>: <em></em> <strong>log1p</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute
<code>log (1 + <var>x</var>)</code>
accurately in the neighborhood of zero.
</p>
<p><strong>See also:</strong> <a href="#XREFlog">log</a>, <a href="#XREFexp">exp</a>, <a href="#XREFexpm1">expm1</a>.
</p></dd></dl>


<a name="XREFlog10"></a><dl>
<dt><a name="index-log10"></a>: <em></em> <strong>log10</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute the base-10 logarithm of each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFlog">log</a>, <a href="#XREFlog2">log2</a>, <a href="Special-Utility-Matrices.html#XREFlogspace">logspace</a>, <a href="#XREFexp">exp</a>.
</p></dd></dl>


<a name="XREFlog2"></a><dl>
<dt><a name="index-log2"></a>: <em></em> <strong>log2</strong> <em>(<var>x</var>)</em></dt>
<dt><a name="index-log2-1"></a>: <em>[<var>f</var>, <var>e</var>] =</em> <strong>log2</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute the base-2 logarithm of each element of <var>x</var>.
</p>
<p>If called with two output arguments, split <var>x</var> into
binary mantissa and exponent so that
<code>1/2&nbsp;&lt;=&nbsp;abs(f)&nbsp;&lt;&nbsp;1</code><!-- /@w -->
and <var>e</var> is an integer.  If
<code>x&nbsp;=&nbsp;0</code><!-- /@w -->, <code>f&nbsp;=&nbsp;e&nbsp;=&nbsp;0</code><!-- /@w -->.
</p>
<p><strong>See also:</strong> <a href="#XREFpow2">pow2</a>, <a href="#XREFlog">log</a>, <a href="#XREFlog10">log10</a>, <a href="#XREFexp">exp</a>.
</p></dd></dl>


<a name="XREFpow2"></a><dl>
<dt><a name="index-pow2"></a>: <em></em> <strong>pow2</strong> <em>(<var>x</var>)</em></dt>
<dt><a name="index-pow2-1"></a>: <em></em> <strong>pow2</strong> <em>(<var>f</var>, <var>e</var>)</em></dt>
<dd><p>With one input argument, compute
2 .^ x
for each element of <var>x</var>.
</p>
<p>With two input arguments, return
f .* (2 .^ e).
</p>
<p><strong>See also:</strong> <a href="#XREFlog2">log2</a>, <a href="#XREFnextpow2">nextpow2</a>, <a href="Arithmetic-Ops.html#XREFpower">power</a>.
</p></dd></dl>


<a name="XREFnextpow2"></a><dl>
<dt><a name="index-nextpow2"></a>: <em></em> <strong>nextpow2</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute the exponent for the smallest power of two larger than the input.
</p>
<p>For each element in the input array <var>x</var>, return the first integer
<var>n</var> such that
2^n &ge; abs (x).
</p>

<p><strong>See also:</strong> <a href="#XREFpow2">pow2</a>, <a href="#XREFlog2">log2</a>.
</p></dd></dl>


<a name="XREFrealpow"></a><dl>
<dt><a name="index-realpow"></a>: <em></em> <strong>realpow</strong> <em>(<var>x</var>, <var>y</var>)</em></dt>
<dd><p>Compute the real-valued, element-by-element power operator.
</p>
<p>This is equivalent to <code><var>x</var>&nbsp;.^&nbsp;<var>y</var></code><!-- /@w -->, except that
<code>realpow</code> reports an error if any return value is complex.
</p>
<p><strong>See also:</strong> <a href="Arithmetic-Ops.html#XREFpower">power</a>, <a href="#XREFreallog">reallog</a>, <a href="#XREFrealsqrt">realsqrt</a>.
</p></dd></dl>


<a name="XREFsqrt"></a><dl>
<dt><a name="index-sqrt"></a>: <em></em> <strong>sqrt</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute the square root of each element of <var>x</var>.
</p>
<p>If <var>x</var> is negative, a complex result is returned.
</p>
<p>To compute the matrix square root, see <a href="Linear-Algebra.html#Linear-Algebra">Linear Algebra</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFrealsqrt">realsqrt</a>, <a href="#XREFnthroot">nthroot</a>.
</p></dd></dl>


<a name="XREFrealsqrt"></a><dl>
<dt><a name="index-realsqrt"></a>: <em></em> <strong>realsqrt</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return the real-valued square root of each element of <var>x</var>.
</p>
<p>If any element results in a complex return value <code>realsqrt</code> aborts and
issues an error.
</p>
<p><strong>See also:</strong> <a href="#XREFsqrt">sqrt</a>, <a href="#XREFrealpow">realpow</a>, <a href="#XREFreallog">reallog</a>.
</p></dd></dl>


<a name="XREFcbrt"></a><dl>
<dt><a name="index-cbrt"></a>: <em></em> <strong>cbrt</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute the real cube root of each element of <var>x</var>.
</p>
<p>Unlike <code><var>x</var>^(1/3)</code>, the result will be negative if <var>x</var> is
negative.
</p>
<p><strong>See also:</strong> <a href="#XREFnthroot">nthroot</a>.
</p></dd></dl>


<a name="XREFnthroot"></a><dl>
<dt><a name="index-nthroot"></a>: <em></em> <strong>nthroot</strong> <em>(<var>x</var>, <var>n</var>)</em></dt>
<dd>
<p>Compute the real (non-complex) <var>n</var>-th root of <var>x</var>.
</p>
<p><var>x</var> must have all real entries and <var>n</var> must be a scalar.
If <var>n</var> is an even integer and <var>x</var> has negative entries then
<code>nthroot</code> aborts and issues an error.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">nthroot (-1, 3)
&rArr; -1
(-1) ^ (1 / 3)
&rArr; 0.50000 - 0.86603i
</pre></div>

<p><strong>See also:</strong> <a href="#XREFrealsqrt">realsqrt</a>, <a href="#XREFsqrt">sqrt</a>, <a href="#XREFcbrt">cbrt</a>.
</p></dd></dl>


<hr>
<div class="header">
<p>
Next: <a href="Complex-Arithmetic.html#Complex-Arithmetic" accesskey="n" rel="next">Complex Arithmetic</a>, Up: <a href="Arithmetic.html#Arithmetic" accesskey="u" rel="up">Arithmetic</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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