Logarithms

log is short for logarithm

when you perform a log function on a number the result is an exponent

a log has a base to it just like the base of an exponent

performing a log function is the inverse of an exponential function

The base of a log is the same as the base of an exponential

log₂ 8= y means the same as 2^y=8

We would read the above as log base 2 of 8

Notice that 2 to the 3rd power is 8, so y=3 in the above equations

so log₂8=3

log₅25 = 2 since 5²=25

if we write a log without a base such as log1000=3, this means the base is 10

Since using a base of 10 is very common we call this the common log.

log1000 means the same as log₁₀1000

Our number system is base 10

10⁰=1 10¹=10 10²=100 10³=1000

So when we write log x it automatically means we are dealing with base 10

Just like subtraction is inverse to addition

Division is inverse to Multiplication

Square root is inverse to squaring

Applying a log with the same base as an exponential is the inverse to using the exponent and can tell us what the exponent is.

For example log250 = x tells us what the exponent of 10^x = 250 would be. Plug this into your calculator to find the exponent.