Answer

Verified

387k+ 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.

Recently Updated Pages

Cryolite and fluorspar are mixed with Al2O3 during class 11 chemistry CBSE

Select the smallest atom A F B Cl C Br D I class 11 chemistry CBSE

The best reagent to convert pent 3 en 2 ol and pent class 11 chemistry CBSE

Reverse process of sublimation is aFusion bCondensation class 11 chemistry CBSE

The best and latest technique for isolation purification class 11 chemistry CBSE

Hydrochloric acid is a Strong acid b Weak acid c Strong class 11 chemistry CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

The Buddhist universities of Nalanda and Vikramshila class 7 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Name 10 Living and Non living things class 9 biology CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Who founded the Nalanda University 1 Mauryan 2 Guptas class 6 social science CBSE