What is a logarithm

This one will be simple. A logarithm is how many times you have to repeatedly divide some number by the denominator until the quotient is a one.

You have a number a that you divide by b and use the quotient as the next division operation's numerator. Carry on with the pattern till you get to a quotient which when divided by b you get one. The number of division operations is the logarithm to the base b of the number a.

For instance, log base 2 of 8 is 3. Since 8/2 is 4 and 4/2 is 2 then finally, 3rd division operation, 2/2 gives us a 1.

That's it. Ain't magic.

Assume all logs are to base 2 from hence forth

Some common laws of logarithms.

• log(b) = x implies 2^x = b
• log(b^2) = 2xlog(b)
• log(bxc) = log(b) + log(c)
• log(b/c) = log(b) - log(c)

Applications of logarithms

• Compression
• Differentiation