What is the value of \( \log_3 81 \)? Options: 1) 2 2) 3 3) 4 4) 5
Answer (1)
To find the value of lo g 3 81 , we need to determine what power 3 must be raised to in order to equal 81.
Identify the bases and exponents: The expression lo g 3 81 is asking, 'To what power must 3 be raised to get 81?'
Recognize a hint of powers of 3: Here, we try to express 81 as a power of 3. Through trial or knowledge, 81 can be expressed as 3 4 .
Evaluate the logarithm: Therefore, lo g 3 81 = lo g 3 ( 3 4 ) .
Apply logarithmic identity: Using the logarithmic identity lo g b ( b x ) = x , because the base of the logarithm (3) and the base of the exponent (3) are the same:
lo g 3 ( 3 4 ) = 4.
Conclusion: Thus, lo g 3 81 = 4 .
Therefore, the value of lo g 3 81 is 4.
The correct multiple-choice answer is Option 3: 4.
