Evaluate log 18 + log6 - log16$^{\frac{1}{2}}$

Analyze the question: We need to combine logs using the laws of logarithms. The expression is log 18 + log 6 − log 16^(1/2).

Concept:

• log a + log b = log(ab)
• log a − log b = log(a/b)
• 16^(1/2) = √16 = 4

Solution:

Step 1: Simplify 16^(1/2) = 4.

Step 2: Rewrite the expression: log 18 + log 6 − log 4

Step 3: Combine: log (18 × 6 / 4) = log (108 / 4) = log 27

Step 4: Express 27 as a power of 3: log 27 = log 3³ = 3 log 3

Answer: 3 log 3, which is option E.

Tip: When you see a log problem, turn every sum into a product and every difference into a quotient, then look for perfect powers (like 27 = 3³, 8 = 2³) to match the options. Also, remember that a fractional power like 16^(1/2) is just a square root.