log644 - log64 = log6(44/4) = log611
Nowadays you cannot do it without a calculator.
log1 + log2 + log3 = log(1*2*3) = log6
That can't really be simplified. I can though be rewritten: Log 6 = x is another way of saying: 10x = 6
log(x) + 4 - log(6) = 1 so log(x) + 4 + log(1/6) = 1 Take exponents to the base 10 and remember that 10log(x) = x: x * 104 * 1/6 = 10 x = 6/1000 or 0.006
To enter a natural log, press the LN button. To enter a log with base 10, press the LOG button. To enter a log with a base other than those, divide the log of the number with the log of the base, so log6(8) would be log(8)/log(6) or ln(8)/ln(6). (The ln is preferred because in calculus it is easier to work with.)
The only base number you are ever likely to come across is base 10. It is the system used by everyone everywhere. It means there are 10 numbers (0,1,2,3,4,5,6,7,8,9) and then they repeat (10,11,12,13,14,15,16,17,18,19). They only other base ever commonly used was base 6. This system would look like 0,1,2,3,4,5,6,10,11,12,13,14,15,16,20,21,22,... In mathematics, changing bases is sometimes useful. For instance in taking logs (logarithms). log10(1000)=3 is easy but not log6(1000)=.77815125038364. This is because we always assume that 1000 is the 1000 in base 10.