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If \[{\log _3}81 = x\], then \[x\] is equal to
A.2
B.3
C.4
D.5

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Last updated date: 20th Jun 2024
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Answer
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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.