Evaluate the logarithm

Question

Evaluate log₂ (1,010) to 4 decimal places.

Answer 1

using the change of base formula,

ln(1010)/ ln(2) = 9.9802

Answer 2

2^2 = 4

2^4 = 4^2 = 16

2^8 = 16^2 = 256

2^16 = 256^2 = 65,536

the log is somewhere between 8 and 16

2^10 = 256x4 =1024

2^9= 256x2 = 512

the log is slightly less than 10, maybe 9.99 or so

they have calculators that can give you the precise log, but mine doesn't have that function

you could change the base

log2(1010) =ln1010/ln2 = 6.91770561/0.69314718= 9.980139586 = 9.9801 rounded to 4 decimals

In general loga(b) = lnb/lna = log10(b)/log10(a) = logz(b)=logz(a). you can change the log of any base to the quotient of the log of any other base, such as e or 10, so you can calculate it on most calculators.