Math

QuestionCalculate log381\log _{3} 81. Choose from: a) 3 b) 9 c) 27 d) 4 e) none of the above.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the value of log381\log{3}81 . We know that logba=c\log{b} a = c if and only if bc=ab^c = a
3. We are given the options a)3, b)9, c)27, d)4, and e) none of the above

STEP 2

We can use the definition of logarithms to set up an equation.c=81^c =81

STEP 3

Now, we can try each of the given options to see which one makes the equation true.
a) If c=3c =3, then 33=273^3 =27, which is not equal to81.
b) If c=9c =9, then 39=196833^9 =19683, which is not equal to81.
c) If c=27c =27, then 3273^{27} is a very large number, which is not equal to81.
d) If c=c =, then 3=813^ =81, which is equal to81.
So, the correct answer is d).

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