Logarithms

Logarithms

Definition:

1. log_a x = N means that a^N = x.
2. log x means log₁₀ x. All log_a rules apply for log. When a logarithm is written without a base it means common logarithm.
3. ln x means log_e x, where e is about 2.718. All log_a rules apply for ln. When a logarithm is written "ln" it means natural logarithm.
    Note: ln x is sometimes written Ln x or LN x.

Common Logarithm

The logarithm base 10 of a number. That is, the power of 10 necessary to equal a given number. The common logarithm of x is written log x. For example, log 100 is 2 since 10² = 100.

Natural Logarithm

The logarithms base e of a number. That is, the power of e necessary to equal a given number. The natural logarithm of x is written ln x. For example, ln 8 is 2.0794415... since e^2.0794415... = 8.


Rules
1. Inverse properties:   log_a a^x = x   and   a^(loga ^x) = x
2. Product:  log_a (xy) = log_a x + log_a y

Examples:

Write each of the following in logarithmic form:

Evaluate the following:

 What number is n?

                               

https://www.youtube.com/watch?v=mQTWzLpCcW0

click the link below for more examples!

References:

http://www.themathpage.com/aprecalc/logarithms.htm#ex4