How do I calculate the closest power of 2 or 10 a number is?

Question

What is the most efficient way to cacluate the closest power of a 2 or 10 to another number? e.g.

3.5 would return 4 for power of 2 and 1 for power of 10

123 would return 128 for power of 2 and 100 for power of 10

0.24 would return 0.25 for power of 2 and 0.1 for power of 10

I'm just looking for the algorithm and don't mind the language.

Answer 1

n^round(log_n(x))

where log_n is the logarithm to base n. You may have to modify the round() depending on how you define "closest".

Note that log_n(x) can be implemented as:

log_n(x) = log(x) / log(n)

where log is a logarithm to any convenient base.