Question 31804
{{{ 10^2 = 100 }}} --> {{{ log(100) = 2 }}}
{{{ 10^3 = 1000 }}} --> {{{ log(1000) = 3 }}}
{{{ 10^4 = 10000 }}} --> {{{ log(10000) = 4 }}}
{{{ 10^5 = 100000 }}} --> {{{ log(100000) = 5 }}}


These are logs to base 10...possibly your "common logs"?


We can do logs to any base. The following are logs to base2... written by me as log_2:
{{{ 2^2 = 4 }}} --> {{{ log_2(4) = 2 }}}
{{{ 2^3 = 8 }}} --> {{{ log_2(8) = 3 }}}
{{{ 2^4 = 16 }}} --> {{{ log_2(16) = 4 }}}
{{{ 2^5 = 32 }}} --> {{{ log_2(32) = 5 }}}


Now one particular number is 2.7182818284590.... is a number that goes on forever...has no end, so how can we write it? Well, we give it a "name", calling it e.


When the log base is the number e, these are called natural logs, since a lot of things in nature follow the mathematical curve of {{{y=e^x}}}


Natural logs are written as ln, eg ln(10) = 2.302585...


Hope this helps.


jon.