Writing log(625) as seperate logs

[jwpaine]

Lets say I had a table of log values (in base 10) from 1 to 20... that I could use to find log(625).....how can I expand this into multiple logs?

Because log addition = multiplication and subtraction = division

I tried this:

log(625) = log(10^2 * 6 + 20 + 5) = log(10^2) + log(6) * log(20) * log(5)

but my calculator gives me 2.70764 when log(625) approx = 2.79588

what have I done wrong?

 

[skeeter]

log(625) = log(10^2 * 6 + 20 + 5) = log(10^2) + log(6) * log(20) * log(5)

log(a*b) = log(a) + log(b) ... but, log(a + b) does not equal log(a)*log(b)


log(625) = log(5⁴) = 4log(5)