Simplify the expression:  $Log_{4}16$ +  $Log_{3}27$ + $Log_{8}4096$

Analyze the question: We need to evaluate three logarithms and add them. Each one asks: "To what power must the base be raised to give this number?"

Concept: log_b(N) = x means b^x = N.

Solution:

1. log₄16: 4² = 16, so log₄16 = 2

2. log₃27: 3³ = 27, so log₃27 = 3

3. log₈4096: Note that 8⁴ = 4096 (8² = 64, 64² = 4096). So log₈4096 = 4

Add them up:

2 + 3 + 4 = 9

Answer: E (9)

Tip: Memorise common powers (2¹⁰ = 1024, 2¹² = 4096, 8⁴ = 4096, 4⁶ = 4096, 16³ = 4096). If you're stuck on a large number, write it in base 2: 4096 = 2¹² and 8 = 2³, so log₈4096 = 12 ÷ 3 = 4. Converting everything to a common prime base is a quick way to handle such questions.