# Lncollect; Lnp1; Local; Log - HP 48gII Advanced User's Reference Manual

Graphing calculator.

## LNCOLLECT

CAS:
Simplify an expression by collecting logarithmic terms.

### LNP1

Type:
Analytic function
Description: Natural Log of x Plus 1 Analytic Function: Returns ln (x + 1).
For values of x close to zero, LNP1(x) returns a more accurate result than does LN(x+1). Using
LNP1 allows both the argument and the result to be near zero, and it avoids an intermediate
result near 1. The calculator can express numbers within 10
For values of x < –1, an Undefined Result error results. For x=–1, an Infinite Result exception
occurs, or, if flag –22 is set, LNP1 returns –MAXR.
Access:
Flags:
Numerical Results (-3), Inifinite Result Exception (-22)
Input/Output:
EXPM, LN

### LOCAL

CAS:
Create local variables.

### LOG

Type:
Analytic function
Description: Common Logarithm Analytic Function: Returns the common logarithm (base 10) of the
argument.
For x=0 or (0, 0), an Infinite Result exception occurs, or, if flag –22 is set (no error), LOG
returns –MAXR.
The inverse of ALOG is a relation, not a function, since ALOG sends more than one argument to
the same result. The inverse relation for ALOG is the general solution:
The function LOG is the inverse of a part of ALOG, a part defined by restricting the domain of
ALOG such that 1) each argument is sent to a distinct result, and 2) each possible result is
achieved. The points in this restricted domain of ALOG are called the principal values of the
inverse relation. LOG in its entirety is called the principal branch of the inverse relation, and the
points sent by LOG to the boundary of the restricted domain of ALOG form the branch cuts of
LOG.
The principal branch used by the hp49g+/hp48gII for LOG(z) was chosen because it is analytic
in the regions where the arguments of the real-valued function are defined. The branch cut for
the complex-valued LOG function occurs where the corresponding real-valued function is
undefined. The principal branch also preserves most of the important symmetries.
You can determine the graph for LOG(z) from the graph for LN (see LN) and the relationship
log z = ln z / ln 10.
...Ã
Access:
Flags:
Principal Solution (-1), Numerical Results (-3), Inifinite Result Exception (-22)
1
HYPERBOLIC LNP
Level 1/Argument 1
x
'symb'
LOG(Z)+2* *i*n1/2.30258509299
of zero, but within only 10
-449
( ´ is the left-shift of the Pkey).
( Ã is the right-shift of the Vkey).
Full Command and Function Reference 3-97
of 1.
–11
Level 1/Item 1
ln (x + 1)
'LNP1(symb)'  