This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

RealExponent

RealExponent[x]
gives .
RealExponent
gives .
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]:=
Click for copyable input
Out[1]=
This is the number such that :
In[2]:=
Click for copyable input
Out[2]=
The base-2 exponent:
In[3]:=
Click for copyable input
Out[3]=
This is the number such that :
In[4]:=
Click for copyable input
Out[4]=
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:
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:
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:
New in 6