Question

Rules that govern the ways that logarithms are simplified and combined are going to be very similar to simplifying and combining rules for what other family of functions?

Exponential
Linear
Rational
Polynomial

Answer 1

They are going to be very similar to rules governing exponential functions.  This is due to the fact that logarithms in essence "cancel" exponents.

Answer 2

Rules that govern the ways that logarithms are simplified and combined are going to be very similar to simplifying and combining rules for the exponential family of function.

This comes from the definition of logarithm itself which says that a logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.

Let us illustrate this by way of an example. We know that 100 can be represented as
`10^2`. Here 10 is the base, 2 is the power and 100 is the given number. Therefore,

`10^2=100`

Likewise, we can represent 1000 as
`1000=10^3`

Now, if we multiply
`10^2` and
`10^3` we will get:
`10^2* 10^3=10^(2+3)=10^5`. We added the powers. Therefore, the logarithm of
`10^5` to the base 10 is 5.

Let us see if we will get the same result by using the rules of logarithms.

`log(10^2* 10^3)=log(10^2)+log(10^3)=2log(10)+3log(10)=2+3=5`

As we can see we got the same result by using the logarithm and the exponential rule, thus, verifying our answer. Similar results can be obtained for other operations of the logarithmic rule.