What is the Difference Between log and Natural log?
🆚 Go to Comparative Table 🆚The main difference between log and natural log (ln) is the base they are defined for. Log represents a logarithm to the base 10, also known as the common logarithm, while ln represents a logarithm to the base e, also known as the natural logarithm. Here are some key differences between log and ln:
- Base: Log is defined for base 10, whereas ln is defined for base e.
- Notation: Log is represented as log10(x), while ln is represented as loge(x) or ln(x).
- Exponential Form: The exponential form for log is 10x = y, while for ln, it is ex = y.
Logarithms are essential for solving equations where an unknown variable appears as the exponent of a number. They are significant in many branches of mathematics and scientific subjects and are used to solve various problems related to finance, economics, and other fields.
Comparative Table: log vs Natural log
Here is a table summarizing the differences between log (logarithm) and ln (natural logarithm):
Feature | Log (logarithm) | Ln (natural logarithm) |
---|---|---|
Base | Log refers to a logarithm to the base 10 | Ln refers to a logarithm to the base e (Euler's number) |
Representation | Log is represented as log10(x) | Ln is represented as loge(x) or ln(x) |
Exponent Form | The exponent form of the common logarithm is 10x = y | The exponent form of the natural logarithm is ex = y |
Interrogative | "At which number should we raise 10 to get y?" | "At which number should we raise e to get y?" |
Logarithms are essential for solving equations where an unknown variable appears as the exponent of a given number. The key difference between log and ln is the base: log is defined for base 10, while ln is denoted for base e, which is an irrational and transcendental number approximately equal to 2.718281828459.
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