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HP 12c Financial Calculator  Logarithm and Exponential Functions
Basic logarithm and exponential relationships
Exponential and logarithm are related functions as expressed by b = a^{x}, where 'x' is unknown power, 'a' is the base
(known), and 'b' is the value resulting from a^{x} (b>0). The expression that isolates 'x' so 'x' can be computed when 'a' and 'b'
are known is:
The restriction a ≠ 1 applies because if a = 1 then the log(a) = 0 generating an undefined value for 'x'. Some of the
properties related to logarithms and exponents are shown in the examples below.
Logarithm and exponential functions on the HP 12c
There are two exponentrelated and one logarithmrelated functions in the HP 12c, and the keys related to these
functions are , and . computes 'y' raised to the 'x' power while computes 'e' raised to the
power of the number in the display ('e' is the Napier's number 2.718281828...). computes the natural
logarithm of the number in the display.
Practice solving logarithm and exponential problems
Example 1
Continuous compounding is often encountered in conversions from a nominal to an effective interest rate.
The following expression is used:
Figure : Expression for calculating the effective interest rate
What is the effective annual rate equivalent to a nominal rate of 6%, compounded continuously?
Solution
The expression below represents the problem:
Figure : Entering the values in the expression
The following keystroke sequence can be used to compute the effective rate:
Answer
A nominal interest rate of 6%, compounded continuously is equivalent to an effective interest rate of 6.18%.
Example 2
When continuous compounding is considered in conversions from effective to nominal interest rate, the
following expression is used:
Figure : Expression for calculating the nominal interest rate
What is the nominal interest rate, compounded continuously, equivalent to an effective interest rate of
6.18%?
Solution
The expression below represents the problem:
Figure : Entering the values in the expression
The following keystroke sequence can be used to compute the effective rate:
Answer
An effective interest rate of 6.18% is equivalent to a nominal interest rate of 6%, compounded continuously.
Example 3
Evaluate the following expressions and find x:
Solution
The original expression in (1) can be rewritten like this:
To find the solution, press:
Keystroke

Display


Figure : Calculating 'x' using expression 1

In expression (2), one of the basic logarithm properties can be applied:
Figure : Expression using basic logarithm properties
So expression (2) is rewritten:
Figure : Entering the values in the expression
To find the solution, press:
Keystroke

Display


Figure : Calculating 'x' using expression 2

In expression (3), the following sequence can be used:
Keystroke

Display


Figure : Calculating 'x' using expression 3

Answer
The answers are:
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