Question

Evaluate the expression: 1/6 * (3 log2^13728 / 1 + 1 / 2 log2^36 + 1 / 3 log2^8).

a) 12
b) 18
c) 24
d) 30

Answer 1

To evaluate the expression, we need to apply the logarithm rules and simplify each term first. The value of the expression is 1.5.

Step-by-step explanation:

To evaluate the expression, we need to apply the logarithm rules and simplify each term first. Let's start by simplifying the logarithms:

1. log2^13728 = log2(13728) ≈ 13.7546
2. log2^36 = log2(36) ≈ 5.1699
3. log2^8 = log2(8) = 3

Next, we can substitute the simplified logarithms back into the expression:

1/6 * (3 * 13.7546 / (1 + 1/2 * 5.1699 + 1/3 * 3))

= 1/6 * (41.2638 / (1 + 2.58495 + 1))

= 1/6 * (41.2638 / 4.58495)

= 1/6 * 9

= 1.5

So, the value of the expression is 1.5. Therefore, the correct answer is a) 12.