Answer:


Explanation:
Part (a)
The common logarithm is the logarithm with base 10. It is often written as log without a specified base:

To rewrite
as a ratio of common logarithms, we can use the change of base formula.
The change of base formula is:

where n is the new base.
In our case:
Substituting the values into the change of base formula gives:

As the common logarithm is often written as log without a specified base, this can also be written as:


Part (b)
The natural logarithm is the logarithm with base e, where e is the Euler's constant approximately equal to 2.7182818 (7 d.p.). It is usually written as "ln":

To rewrite
as a ratio of natural logarithms, we can use the change of base formula.
The change of base formula is:

where n is the new base.
In our case:
Substituting the values into the change of base formula gives:

As the natural logarithm is often written as "ln", this can also be written as:
