Difference Between Ln And Log (Logarithm V/S Natural Log), Important Properties, JEE 2024
Difference Between Ln and Log : Read about the basic difference between ln and log. Learn the properties, uses and values of the natural log(ln) and log.
Shrivastav 16 Jan, 2024
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Difference Between Ln And Log : To know the difference between ln and log, it is very important to define the terms. The logarithm of a number is the exponent that must be increased to get that number from another base value.
For example, 1000's logarithm in base 10 is 3, since 1000=10 3 . The common logarithm, which has a base of 10 and is widely used in research and engineering, is known as the logarithm to base b, while the natural logarithm, which has the constant e (2.718281828) as its basis and is expressed as ln(x) or loge (x). The natural logarithm of a number x represents the power to which e must be increased in order to equal that number. For instance, ln (7.389…) is 2 because e 2 = 7.389. The natural log of e itself (ln(e)) is 1 since e 1 =e, while the natural logarithm of 1 (ln (1)) is 0, because e 0 =1. A natural logarithm may be defined as the power to which the base 'e' must be raised to generate a number known as the log number. Here e represents the exponential function. It was first found in the 17th century by John Napier, who also developed and formulated the logarithm theory. Before we get into the fundamental difference between ln and log , let's first define log and ln. Achieve JEE excellence with PW JEE Online Course . Join now to fulfill your engineering dreams!Definition of Log
In mathematics, the logarithm represents the inverse function of exponentiation. In other terms, a log is defined as the power at which a number must be increased to get the other number. This is sometimes called the base-10 logarithm or the common logarithm. The logarithm has the following general formula : Loga(y) = x It can also be written as. a x = yDefinition of Ln
The term "natural logarithm" refers to Ln. It is sometimes referred to as the base-e logarithm. In this case, the constant e stands for an irrational and transcendental number that is roughly equivalent to 2.71828182845. The expression of the natural logarithm (ln) is either log e x or lnx.Difference Between ln and Log
Difference Between ln and Log : Knowing the difference between log and natural log is important in order to solve logarithmic problems. Having an in-depth knowledge of exponential functions might be helpful in understanding a lot of concepts. Here is a table that highlights some of the key difference between ln and log:| Difference Between ln and Log | ||
| Property | Logarithm (log) | Natural Logarithm (ln) |
| Definition | Refers to a logarithm to the base 10 | Refers to a logarithm to the base e |
| Alternative Names | Common logarithm | Natural logarithm |
| Representation | log10 (x) | loge (x) |
| Exponential Form | 10 x = y | E x = y |
| Interrogative Statement | "At which number should we raise 10 to get y?" | "At which number should we raise Euler’s constant to get y?" |
| Usage | Mostly used in physics | Much less use in physics |
| Mathematical Representation | log base 10 | log base e |
Properties of Logarithm
- Log b m + Log b n = Log b (mn).
- Log b m - Log b n = Logb (m/n)
- Log b (m n ) = nlog b m .
- Log a m / log a = log b m
Various Rules of Ln
Quotient Rule: ln(x/y) = ln(x) - ln(y) The natural log of the division of x and y is the difference between ln x and ln y. Example: ln(10/5) = ln(10) - ln(5) Reciprocal Rule: ln(1/x) = −ln(x) The natural log of the reciprocal of x is equivalent to the inverse of the ln of x. Example: ln(⅓) = -ln(3). Power Rule: Ln x y = y* lnx The natural log of x raised to the power of y equals y times the ln of x. Example: ln(4²) = 2 * ln(4). Looking For Best Books for the JEE Exam Preparation?Value Difference Between Ln and Log
Value Difference Between Ln and Log : The values of ln and log for the first 10 numbers are computed below in the tables, check the difference in value between ln and log:Value of Log from 1 to 10
The Value of Log from 1 to 10 may be used to get the logarithm values of greater integers. The values from log 1 to 10 to base 10 are as follows:| Value Difference Between Ln and Log | |
| Common Logarithm of a Number (log 10 x) | Log Value |
| Log 1 | 0 |
| Log 2 | 0.3010 |
| Log 3 | 0.4771 |
| Log 4 | 0.6020 |
| Log 5 | 0.6989 |
| Log 6 | 0.7781 |
| Log 7 | 0.8450 |
| Log 8 | 0.9030 |
| Log 9 | 0.9542 |
| Log 10 | 1 |
Value of Ln from 1 to 10
When calculating the natural logarithm of bigger integers, the value of Ln, which ranges from 1 to 10, might be helpful. The value of ln 1 to 10 is shown in this table using the natural logarithm log e x.| Value of Ln from 1 to 10 | |
| Natural Logarithm of a Number log e x | Ln Value |
| ln (1) | 0 |
| ln (2) | 0.693147 |
| ln (3) | 1.098612 |
| ln (4) | 1.386294 |
| ln (5) | 1.609438 |
| ln (6) | 1.791759 |
| ln (7) | 1.94591 |
| ln (8) | 2.079442 |
| ln (9) | 2.197225 |
| ln (10) | 2.302585 |
Difference Between ln and Log FAQs
Q.1: Is Ln the same as the Log Base 10?
Ans. A logarithm, represented as logb(x), is the number needed to increase b to obtain x. In mathematics, certain logarithms appear more often than others, and we categorize them as specific sorts of logarithms based on the value of their base.
Q.2: What is a log of zero?
Ans. Log 0 has no specified value. Since you can never achieve zero by raising something to the power of anything, it is not a real number.
Q.3: Can ln be zero?
Ans. For all non-positive values, including zero, the natural logarithm (ln) of that integer is undefinable.
Q.4: What is the power rule of log?
Ans. The power rule of logs says that if the argument of a logarithm has an exponent, then the exponent can be brought to the front of the logarithm.
Q.5: What is 1 divided by infinity?
Ans. Any integer is equivalent to zero when divided by infinity. It is not possible to divide a number by infinity as infinity is an idea rather than a real number.
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