Value of Log 1: Logarithmic Functions, Value of In 1, Logarithmic Values

Each value of the log is unique and is positive. The value of log₁₀1 is equal to 0 which can be estimated using the logarithm function, which is one of the most important functions in mathematics. The log functions are commonly used for solving lengthy problems or to reduce the complexity of the problems by reducing the operations from division to subtraction and multiplication to addition.

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In mathematics, logarithms were used earlier by the researchers to transform multiplication and division problems into addition and subtraction problems before the concept of calculus came into consideration. Logarithms are mostly used in science as well as mathematics as both the subjects contend with large numbers.

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Logarithmic Functions

The logarithm value of a number is the power of the exponent by which the same must be raised to return an equivalent value of the given number. The logarithmic functions are the reverse of exponential functions.

Logarithmic Functions

The classification of logarithmic function is done in two types which are:

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Common Logarithmic Function

A common logarithmic function is also known as a decade logarithm and decimal logarithm and has a fixed base of 10. A common logarithm for a number N is expressed as log₁₀ N or log N. If the value of log N is equal to x, then in exponential form the logarithmic form can be represented as 10^x=N.

Logarithmic Function: Common and Natural

Natural Logarithmic Function

For a number N, the natural logarithm is represented as the power of an exponent to which it has to be raised to be equivalent to the value of N. The natural logarithm is generally used in pure mathematics for example calculus. The value of N=x is similar to the value N= e^x.

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Properties of Common Logarithm

In mathematics, there are four laws of common logarithms that are similar to the properties of all logarithms. These laws help in solving a complex problem to obtain the solution for it. The four Logarithmic laws have been mentioned in the list below:

Product Rule Law: Iog_a (MN) = log_a M + log_a N

Quotient Rule Law: Iog_a (M/N) = Iog_a M - Iog_a N

Power Rule Law: Iog_a Mn = n Iog_a M

Change of Base Rule Law: Iog_a M = Iogb M × Iog_a b

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Properties of Natural Logarithm

The properties of natural logs are similar to other logarithmic values. The list of properties are mentioned below:

Product law: According to the product law, Ln (ab) = ln (a) + ln (b)

Quotient rule: As per the quotient law, Ln (a/b) = ln (a) – ln (b)

Reciprocal rule: In reciprocal law, Ln (1/a) = -ln (a)

Power rule: In power law, ln (ab) = b ln (a)

There are few other properties of the natural log which are mentioned in the list below:

• e ^{ln (x)} = x
• ln (e ^x) = x
• ln (e) = 1
• ln (∞) = ∞
• ln (1) = 0

Also Check:

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Value of Log 1

As per the definition of logarithm function, the value of loga b = x can be written in the form of an exponential function which is given below:

Then, ax = b

For finding the value of log 1, let’s ruminate the base of the log as 10 since no base value is defined here. Henceforth, we can write log 1 as log₁₀ 1.

Now, by the definition of the logarithm, we get the values of a and b as 10 and 1 respectively. Such that, log10 ^x = 1.

Through the logarithm rule, we can rephrase the above expression as 10^x = 1

It is well-known that any number raised to the power 0 is equivalent to 1. Thus, 10 raised to the power 0 will make the above expression true.

Thus, 10⁰ = 1

This will be a situation for all the base values of the log, where the base raised to the power 0 will return 1.

Therefore, the value of log 1 is equivalent to zero.

Log₁₀ 1= 0

‘a’ could be any positive value apart from 1.

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Value of ln 1

Just like the value of log 1, we can also represent the value of natural log of 1, i.e. ln 1.

Ln (b) = log_e (b)

Consequently, Ln(1) = log_e(1)

Or we can write e^x = 1

Therefore, e⁰ = 1

Hence, Ln(1) = log_e(1) = 0

Also Read: Remainder Theorem

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Logarithmic Values

The list of logarithmic values numbers from 1 to 10 has been mentioned in the table below:

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Things to Remember

• The logarithm can be determined as the exponent or power to which a base must be raised to get a new number.
• A logarithm is an appropriate approach for expressing large numbers.
• There are two types of logarithmic functions i.e. common and natural logarithm.
• The value of log 1 base 10 i.e. log101 = 0.

Also Check:

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