Question

Rewrite each of the following expressions as a single logarithm. That is, each answer should contain only one log (or ln) expression.

a. 4log6(x)+log6(y)=
b. n(x)+ln(y)−ln(z)=

Answer 1

To rewrite logarithmic expressions as a single logarithm, one must utilize properties of logarithms. For expression a, the properties allow for the combination into log6(x4y). Expression b is combined into ln(xy/z) using similar logarithmic rules.

Step-by-step explanation:

The question requires us to rewrite expressions involving logarithms as a single logarithm. We will use properties of logarithms to do so.

Expression a: 4log6(x) + log6(y)

Using the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number, we can rewrite 4log6(x) as log6(x4). Then, applying the property that the logarithm of a product is the sum of the logarithms, we get:

log6(x4y)

Expression b: ln(x) + ln(y) - ln(z)

Again, we will use the properties of logarithms. Since the logarithm of a product is the sum of the logarithms, we can combine the first two terms. Then, because the logarithm of a number resulting from the division of two numbers is the difference between the logarithms of the two numbers, we can subtract the third term, resulting in:

ln(xy/z)

Therefore, the final answers for the expressions given are log6(x4y) and ln(xy/z), respectively.