How to Put A Logarithm Into A Calculator
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Reviewed by Calculator Editorial Team
Logarithms are essential in mathematics, science, and engineering. This guide explains how to input and calculate logarithms on different types of calculators, including scientific, graphing, and online calculators.
Basic Logarithm Calculation
A logarithm answers the question: "To what power must a base number be raised to obtain another number?" The general form is:
logb(a) = c means bc = a
For example, log2(8) = 3 because 23 = 8.
Step-by-Step Instructions
- Press the "LOG" button on your calculator.
- Enter the base number (b) first.
- Press the comma or comma key (depending on your calculator model).
- Enter the argument number (a).
- Press the equals (=) button to get the result (c).
Most scientific calculators use the comma key (,) to separate the base and argument in logarithm calculations.
Using Scientific Notation
For very large or very small numbers, use scientific notation:
log10(1,000,000) = log10(1 × 106) = 6
On most calculators:
- Enter the coefficient (1 in this case).
- Press the "EE" or "EXP" button.
- Enter the exponent (6 in this case).
- Press the "LOG" button.
- Press the equals (=) button.
Natural Logarithm (ln)
The natural logarithm uses base e (approximately 2.71828):
ln(a) = loge(a)
To calculate on most calculators:
- Press the "LN" button.
- Enter the argument number (a).
- Press the equals (=) button.
Common Logarithm (log)
The common logarithm uses base 10:
log(a) = log10(a)
To calculate on most calculators:
- Press the "LOG" button.
- Enter the argument number (a).
- Press the equals (=) button.
Logarithm Properties
Key properties to remember:
- logb(b) = 1
- logb(1) = 0
- logb(bx) = x
- logb(xy) = logb(x) + logb(y)
- logb(x/y) = logb(x) - logb(y)
- logb(xy) = y × logb(x)
These properties can simplify complex logarithm calculations by breaking them into simpler parts.
Frequently Asked Questions
What is the difference between log and ln?
The main difference is the base: log uses base 10 while ln uses base e (approximately 2.71828). Both are common logarithm functions with different applications.
How do I calculate logarithms with negative numbers?
Logarithms of negative numbers are not defined in real numbers. You can only calculate logarithms of positive real numbers.
What if my calculator doesn't have a LOG button?
If your calculator doesn't have a dedicated LOG button, you can use the natural logarithm (LN) function and convert the result using the change of base formula: logb(a) = ln(a)/ln(b).
How accurate are calculator logarithms?
Most scientific calculators provide accurate results to about 10 decimal places. For higher precision, consider using software or programming languages with arbitrary precision arithmetic.