Introduction to Logarithms with Base 10 and e
Key points
- Logarithms are the inverse of exponents, so they can be used to solve for unknown values in n exponential expression.
- Often, logarithms have a base of 10, in which case the base is not written.
- They may also have a base of e, in which case they are written as ln instead of log.
- If logarithms do not have a base of 10 or e, then the base must be written as part of the logarithmic expression.
- They may also have a base of e, in which case they are written as ln instead of log.
Logarithms are the inverse of exponents, and are used to find the unknown power applied to a base in an exponential expression.
- In the example to the right, 2 to the fourth power is rewritten as a logarithmic expression, which is used to find the exponent of four.
- 2 is the base. In an exponential expression, it is being raised to a power, and in the logarithmic expression, it is written as a subscript next to the log.
- 16 is the argument. It is the value of the exponential expression, and is written in parentheses.
- 4 is the exponent, which is the value of the logarithmic expression.
The base of an exponent is the number that is elevated to a certain power in an exponential expression. It is a key element of a logarithmic expression.
- A commonly seen base is 10. In a logarithmic expression, a base of 10 is not written. If there is a logarithm that is written without a base, assume that the base is 10.
- Another common base is e, or Euler’s number. If the base of a logarithm is 10, it is written as ln.
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