How do you simplify $\ln {e^2}$?
Answer
628.5k+ views
Hint: To evaluate any logarithmic value first convert them into general form of the logarithmic function and solve. The general form is ${\log _a}b = c \Leftrightarrow {a^c} = b$
Complete step-by-step answer:
The objective of the problem is to evaluate the value of $\ln {e^2}$.
About logarithm:
The logarithm is the inverse function of the exponential. The logarithm simply counts the occurrence of the same factor in repeated multiplication. There are two types of logarithms. They are common logarithm and natural logarithm
Common logarithm: A common logarithm has a fixed base . The fixed base is 10. The common logarithms are denoted as ${\log _{10}}a$ or simply $\log a$. These common logarithms are also called decimal logarithms.
Natural logarithm: The natural logarithm of a number is equal to the power of “e” . where is equal to the 2.718281. it is known as the Napier constant. The natural logarithm is denoted as $A = {e^x}$. Where A is any number.
To evaluate the value first convert the logarithmic function to the general form of the function. The general form is ${\log _a}b = c \Leftrightarrow {a^c} = b$.
Now let us consider \[\ln {e^2} = c\].
Since it is a natural logarithm we can take a value as e.
By definition it only happens when ${e^c} = {e^2}$
Since bases are equal the power must be equal.
Therefore, $c = 2$
Thus, the value of $\ln {e^2}$ is 2.
Note: We can also solve this simply by using the power rule of logarithms. The power rule of logarithms is $\log \left( {{a^b}} \right) = b\log a$. Logarithms are used in solving exponentials of earthquakes, the brightness of stars and so on.
Complete step-by-step answer:
The objective of the problem is to evaluate the value of $\ln {e^2}$.
About logarithm:
The logarithm is the inverse function of the exponential. The logarithm simply counts the occurrence of the same factor in repeated multiplication. There are two types of logarithms. They are common logarithm and natural logarithm
Common logarithm: A common logarithm has a fixed base . The fixed base is 10. The common logarithms are denoted as ${\log _{10}}a$ or simply $\log a$. These common logarithms are also called decimal logarithms.
Natural logarithm: The natural logarithm of a number is equal to the power of “e” . where is equal to the 2.718281. it is known as the Napier constant. The natural logarithm is denoted as $A = {e^x}$. Where A is any number.
To evaluate the value first convert the logarithmic function to the general form of the function. The general form is ${\log _a}b = c \Leftrightarrow {a^c} = b$.
Now let us consider \[\ln {e^2} = c\].
Since it is a natural logarithm we can take a value as e.
By definition it only happens when ${e^c} = {e^2}$
Since bases are equal the power must be equal.
Therefore, $c = 2$
Thus, the value of $\ln {e^2}$ is 2.
Note: We can also solve this simply by using the power rule of logarithms. The power rule of logarithms is $\log \left( {{a^b}} \right) = b\log a$. Logarithms are used in solving exponentials of earthquakes, the brightness of stars and so on.
Recently Updated Pages
Write structures of the following compounds i 2 Chloro3methylpentane class 11 chemistry CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

Explain the Treaty of Vienna of 1815 class 10 social science CBSE

A Paragraph on Pollution in about 100-150 Words

XIX+XXX A 49 B 51 C 55 D 44 class 5 maths CBSE

If x a + bt + ct2 where x is in meters and t is in class 11 physics CBSE

Trending doubts
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Find the value of the expression given below sin 30circ class 11 maths CBSE

What do you mean by retardation What is its SI uni class 11 physics CBSE

Draw a diagram of nephron and explain its structur class 11 biology CBSE

10 examples of friction in our daily life

Difference between physical and chemical change class 11 chemistry CBSE

