Exp; Alog; Expm1 - HP 39g Master Manual

Some further functions are available in the Hyperbolic group of functions.
They are duplicates of functions available on the face of the calculator but
give more accurate answers. They would primarily be of use to those
people, such as architects and engineers, for whom high accuracy is
paramount. These are:
EXP(num)
This function gives a more accurate answer
than the key labeled e^ which appears above the LN key on the calculator.
As you can see on the right, the difference is normally not detectable even to
12 significant figures.
The difference is only apparent for some
values and even then is hardly earth-
shattering.
ALOG(num)
This function provides the same result as the
key labeled 10^ on the keyboard above the
LOG key. It is another function giving greater
accuracy than the one it 'replaces'. This
greater accuracy would never be required in a
school setting.
EXPM1(num)
This function is designed to be more accurate when anti-logging very small
e − (EXPM1: exp
values close to zero. It gives the value not of but of
x x
e 1
minus 1). You may wonder how this is an advantage, since you must then
add 1 to obtain the correct answer, but a look at the screen opposite will
show you.
As you can see, the normal keyboard function
e^ gives an answer to of 1·0000003.
0.0000003
e
This gives the impression that it is an exact
value (since it doesn't show a full 12 significant
digits). The true answer is 1·000000300000045.... but the final digits have
e − ,
been lost in the rounding off to 12 sig. figures. By giving an answer of
x
1
the leading 1 is lost, freeing the calculator to show more accuracy by
dropping the leading six zeros. This is not normally be needed.
260