What is log base 2 of 8?
The log base 2 of 8 is 3, because 2 raised to the power of 3 equals 8.
Log Base 2 Calculator
6
Result
—
Floor
—
Ceiling
—
Bit Length
—
Exact Power?
—
How to calculate log base 2 of 8
1
First, identify the target value x = 8.
2
Apply the change-of-base formula:
log₂(x) = ln(x) / ln(2).3
Calculate the natural logarithms:
ln(8) ≈ 2.079442
ln(2) ≈ 0.693147
ln(8) ≈ 2.079442
ln(2) ≈ 0.693147
4
Divide the values to get the final result: 3.
Nearby Log Base 2 Values
| Value | log₂(x) |
|---|---|
| 8.0 | 3.000000 |
| 8.1 | 3.017922 |
| 8.2 | 3.035624 |
| 8.3 | 3.053111 |
| 8.4 | 3.070389 |
| 8.5 | 3.087463 |
| 8.6 | 3.104337 |
| 8.7 | 3.121015 |
| 8.8 | 3.137504 |
| 8.9 | 3.153805 |
Related Log Base 2 Calculations
Tips to Quickly Calculate Log base 2 of 8
1
Check whether 8 is close to a power of 2.
2
If 8 equals 2ⁿ, then log₂(x) = n.
3
For large numbers, compare with nearby powers like 512, 1024, or 2048.
4
Use bit-length intuition for fast approximation.
FAQs about log base 2 of 8
It is 3.
Yes, it is an exact power of 2.
Because 2 raised to the power of 3 equals 8.
It is widely used in computer science, binary systems, and algorithms.