Logarithms(log) and natural logarithms(ln) are fundamental mathematical concepts that simplify complex calculations involving exponential relationships Logarithms are essential for solving equations where an unknown variable appears as the exponent of some other quantity.
A logarithm can have any positive base, with the common log having a base 10, while the natural log exclusively uses the mathematical constant (e≈2.718) as its base.
Example- log of base 2 is written as log2 while log of base e is represented as loge= ln (natural log).
Differences Between Log and Ln
Some of the important differences between Log and natural log are given below:
log | ln |
|---|---|
| Log generally refers to a logarithm to the base 10 | Ln generally refers to a logarithm to the base e |
| Also known as the common logarithm | Also called the natural logarithm |
| The common log is represented as log10(x) | The natural log is represented as loge(x) |
| The exponential form for this log is 10x = y | It has the exponential form as ex = y |
| The interrogative statement for the common logarithm is “At which number should we raise 10 to get y?” | The interrogative statement for the natural logarithm is “At which number should we raise Euler’s constant number to get y?” |
| It is mostly used in physics as compared to ln | It has much less use in physics |
| It is represented as log base 10 in math | This is represented as log base e. |
Step to Convert Log into ln
To convert the common log ( log) into natural log(ln) we can simply use the base change formula to change the base from 10 to e.
Base change formula for Logarithm: logba = logca / logcb
To convert Log10(x) into ln
ln(x) = \frac{\log_{10}(x)}{\log_{10}(e)}
To convert lne(x) into Log:
\log_{10}(x) = \frac{\ln_{e}(x)}{\ln_{e}(10)}
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