Built-in Mathematica Symbol

RealExponent

RealExponent[x]
gives

.

RealExponent[x, b]
gives

.

MORE INFORMATION

If x is an approximate number consistent with zero, then RealExponent[x] gives -Accuracy[x].

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

RealExponent automatically threads over lists.

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

:

The base 10 exponent for a number

:

In[1]:=

Out[1]=

This is the number

such that

:

The base 2 exponent:

This is the number

such that

:

In[4]:=

Out[4]=

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:

RealExponent automatically threads over lists:

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: