# RealExponent

RealExponent[x]

gives .

RealExponent[x,b]

gives .

# Examples

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## Basic Examples(1)

The base 10 exponent for a number :

This is the number such that :

The base-2 exponent:

This is the number such that :

## Scope(8)

The real exponent for an arbitrary-precision number:

The result of RealExponent is given as a machine number whatever the precision of :

The real exponent for an exact number:

The real exponent for an exact numeric quantity:

Real exponent for zeros:

This is -Accuracy[x]:

The same is true for arbitrary-precision zeros:

Also for exact zero:

The real exponent for different bases:

The base can be any number strictly greater than 1:

The base can be an exact numeric quantity:

## Applications(2)

Determine quickly if a power will overflow:

This predicts that the power can be represented:

A larger power will not work:

Determine quickly the largest power tower that will not overflow for a given number:

## Properties & Relations(4)

For any approximate number x, RealExponent[x] is equal to Precision[x]-Accuracy[x]:

Also true for arbitrary-precision numbers:

If x is an approximate zero, then RealExponent[x] gives -Accuracy[x]:

This is the same as saying that the identity RealExponent[x] is equal to Precision[x]-Accuracy[x]:

Since precision is zero for approximate zeros:

The real exponent of a product is the sum of the real exponents:

The real exponent of a power is the real exponent of the base times the power:

Wolfram Research (2007), RealExponent, Wolfram Language function, https://reference.wolfram.com/language/ref/RealExponent.html.

#### Text

Wolfram Research (2007), RealExponent, Wolfram Language function, https://reference.wolfram.com/language/ref/RealExponent.html.

#### CMS

Wolfram Language. 2007. "RealExponent." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RealExponent.html.

#### APA

Wolfram Language. (2007). RealExponent. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RealExponent.html

#### BibTeX

@misc{reference.wolfram_2021_realexponent, author="Wolfram Research", title="{RealExponent}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/RealExponent.html}", note=[Accessed: 17-May-2022 ]}

#### BibLaTeX

@online{reference.wolfram_2021_realexponent, organization={Wolfram Research}, title={RealExponent}, year={2007}, url={https://reference.wolfram.com/language/ref/RealExponent.html}, note=[Accessed: 17-May-2022 ]}