Question

use the product, quotient, and power rules of logarithms to rewrite the equation as a single logarithm.

Answer 1

We are given the following expression:

$\log a-3\log b+4\log c$

we are asked to simplify this expression. To do that we will first use the following property:

$a\log b=\log ^{}b^a$

we will apply this to the second and third terms, like this:

$\log a-\log b^3+\log c^4$

Now we will use the following property:

$\log a-\log b=\log (\frac{a}{b})$

we will use this property for the first and second terms:

$\log (\frac{a}{b^3})+\log c^4$

Now we will use the following property:

$\log a+\log b=\log ab$

We will use the property in the last two terms, like this:

$\log (\frac{ac^4}{b^3})$

And thus, we have simplified the logarithmic expression into one single logarithm