Log Base 2 of 16

What is log base 2 of 16?
log₂(16) = 4
4 is the log base 2 of 16.

Use in Mathematics: Log Base 2 of 16
The below are some of the mathematical applications where log base 2 of 16 can be used:

1. to solve exponential equations where the unknown exponent y satisfies 2^y = 16.
2. to simplify complex multiplication or division operations into addition or subtraction of logarithms.
3. to measure logarithmic scale changes, time complexity of algorithms, and calculus functions.

1. By logarithmic definition, log_b(x) = y means b^y = x. Here, 2⁴ = 16.
2. Change of base rule allows converting to natural log (ln) or common log (log₁₀): log₂(16) = ln(16) / ln(2) = log₁₀(16) / log₁₀(2) = 4.
3. Logarithms are defined only for a positive base (b > 0, b ≠ 1) and a positive argument (x > 0).

This step-by-step solution is one of the simple methods to easily understand how to find what is the Log Base 2 of 16, provided along with the use cases of mathematics and real-world problems.

Formula: log₂ 16
log_b(x) = y, if b^y = x

Input:
x = 16
b = 2

step 1 Find the prime factors for 16:
Express 16 in terms of base 2: 16 = 2⁴
log₂(16) = log₂(2⁴)

step 2 Apply logarithm property of multiplication/power:
log₂(16) = log₂(2⁴) = 4 log₂(2)
= 4 log₂(2)

step 3 Use the log table to find and apply the log values:
= 4 x 1

step 4 Find the sum:
= 4
log₂(16) = 4