Log Base 2 Calculator

The base-2 logarithm, written log2(x), answers the question: what exponent must be applied to 2 to produce x? For example, log2(32) equals 5 because 2 raised to the fifth power is 32. The function reverses exponentiation with base 2, so log2(2 to the power y) equals y. This calculator accepts any positive real number and returns the corresponding exponent, including negative and fractional exponents. Powers of two have integer logarithms. Values 1, 2, 4, 8, 16, and 32 produce 0, 1, 2, 3, 4, and 5 respectively. Numbers between consecutive powers produce decimal results. For example, 10 lies between 8 and 16, so its binary logarithm lies between 3 and 4. Positive values below one have negative results because negative powers of two are fractions: log2(0.5) is -1 and log2(0.25) is -2. The real-valued domain of a logarithm contains only positive numbers. Zero has no finite logarithm because no finite power of 2 equals zero, and negative numbers require complex logarithms outside this calculator's scope. The change-of-base identity log2(x) = ln(x) / ln(2) allows the value to be computed using natural logarithms. The output is rounded to ten decimal places for readability, while calculations use JavaScript's full double-precision arithmetic. Binary logarithms are fundamental in computer science because digital systems group information in powers of two. They measure information in bits, describe the height of balanced binary trees, estimate divide-and-conquer algorithm steps, determine storage address widths, and help choose capacities such as buffers or hash tables. In mathematics they are also useful for exponential equations, growth comparisons, and scale analysis. To verify an answer y, calculate 2 raised to y and confirm that it returns the original input. When the result is an integer, the input is an exact power of two; otherwise the calculator identifies it as an approximate non-integer exponent.