Question

Which is equivalent to log Subscript 2 Baseline n = 4?

A)log n = StartFraction log 2 Over 4 EndFraction
B)n = StartFraction log 2 Over log 4 EndFraction
C)n = log 4 times log 2
D)log n = 4 log 2

Answer 1

• D) log n = 4 log 2

Explanation:

Given

• log₂ n = 4

Compare the given with the options to identify equivalents

A)

• log n = log 2 / 4
• log₂ n / log₂ 10 = 1/ log₂ 10 ÷ 4
• log₂ n = 1/4

Not equivalent

B)

• n = log 2 / log 4
• n log 4 = log 2
• n log₂ 4 / log₂ 10 = 1 / log₂ 10
• n log₂ 4 = 1

Not equivalent

C)

• n = log 4 × log 2
• n = log₂ 4/ log₂ 10 × 1/ log₂ 10
• n = 2 /(log₂ 10)²
• n (log₂ 10)² = 2

Not equivalent

D)

• log n = 4 log 2
• log₂ n / log₂ 10 = 4 × 1/log₂ 10
• log₂ n = 4

Equivalent