How would I calcualte these in a calculator to find the Logarithm of these abd round to four decimal places?

log 8

1og 93,100

log 0.082

It depends on the calculator and also the kind of log you are supposed to do.

There are two different kinds of logs in use on calculators, the logarithm to the base 10, better known as common logarithms, and natural logarithm

Common logarithm used to be the tool for calculations. When 10 is raised to a power a to get the number N, i.e.
N=10a,
then a is the common logarithm of N, or
a=log10(N).
For example,
log10100 = 2

Natural logarithm is of great use in calculation of exponential decays, radioactive half-lifes, and other natural phenomenona. It is essentially similar to the common logarithm, except the base 10 is replaced by the constant e which has a value of approximately 2.718281828...
Thus
loge10 = 2.302585...
logee = 1

Common log is written as log10, or simply log.
Natural log is written as ln, or unfortunately also log.
It is possible to have a confusion when using a calculator. So the best bet is to find log(10) to see if you get 1 (common log) or 2.3025... (natural log).

On algebraic calculators, you only need to put in the number follow by the key log (or ln, or log10).
On calculators with RPN (reversed Polish notation, such as Hewlett Packard), you would put in the number, press enter to put it in the register, then press the function log, or ln or log10.

For verification purposes, here are some examples:
log10(93100)=4.9689
ln(93100)=11.4414