Answer
Verified
421.8k+ views
Hint: Here we need to find the value of the variable. We will use the basic properties of the logarithm function to simplify the given problem. Here logarithm function is defined as the inverse function of the exponential function. We will use the properties of logarithm and we will simplify the expression further to get the value of the given variable.
Complete step-by-step answer:
It is given that \[{\log _3}81 = x\] and here, we have to find the value of the variable \[x\].
Here, we will use the properties of the logarithm function to simplify it further.
We can write 81 in the form of exponential as \[{3^4}\].
Now, we will substitute this value in the given expression. Therefore, we get
\[ \Rightarrow {\log _3}{3^4} = x\]
Now, using the property of logarithm \[{\log _a}{a^c} = c\] in the above equation, we get
\[ \Rightarrow 4 = x\]
Thus, we get
\[ \Rightarrow x = 4\]
Therefore, the value of the given variable \[x\] is equal to 4.
Hence, the correct option is option C.
Note: To solve such types of problems, we need to remember the basic properties of the logarithm function. A logarithm is defined as a quantity which represents the power to which a fixed number i.e. the base can be raised to produce a given number. We can also define a logarithm as a function which is the inverse of the exponent function. Here inverse means a function that does the opposite. For example- Subtraction is the inverse of addition; division is the inverse of Multiplication and so on. We can also convert the logarithm function into exponential function when we find the question to get easily solved by using the exponential function.
Complete step-by-step answer:
It is given that \[{\log _3}81 = x\] and here, we have to find the value of the variable \[x\].
Here, we will use the properties of the logarithm function to simplify it further.
We can write 81 in the form of exponential as \[{3^4}\].
Now, we will substitute this value in the given expression. Therefore, we get
\[ \Rightarrow {\log _3}{3^4} = x\]
Now, using the property of logarithm \[{\log _a}{a^c} = c\] in the above equation, we get
\[ \Rightarrow 4 = x\]
Thus, we get
\[ \Rightarrow x = 4\]
Therefore, the value of the given variable \[x\] is equal to 4.
Hence, the correct option is option C.
Note: To solve such types of problems, we need to remember the basic properties of the logarithm function. A logarithm is defined as a quantity which represents the power to which a fixed number i.e. the base can be raised to produce a given number. We can also define a logarithm as a function which is the inverse of the exponent function. Here inverse means a function that does the opposite. For example- Subtraction is the inverse of addition; division is the inverse of Multiplication and so on. We can also convert the logarithm function into exponential function when we find the question to get easily solved by using the exponential function.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE