Question 73437
To evaluate a log that doesn't have a base of 10, you would use the change of base formula
{{{log_[b](a)=(log(a))/(log(b))}}}Where the logs on the right are logs of base 10. So if I have 
{{{log_[2](1000)}}} It would look like this with the change of base formula
{{{log_[2](1000)=(log(1000))/(log(2))}}}
So if we evaluate log(1000) we get 3 (10^3=1000) and if we evaluate log(2) we get 0.30103 approximately
So
{{{log_[2](1000)=(log(1000))/(log(2))=3/0.30103=9.96578}}}Approximately
So {{{log_[2](1000)}}} (or the log base 2 of 1000) is approximately equal to 9.96578
Check:
{{{2^x=1000}}}If we plug in 9.96578 for x we should get 1000
{{{2^(9.96578)=1000}}}
{{{999.99999=1000}}} Which is very close to true, since we have round off errors this is good enough.
Hope this makes sense.