Question

Expand the logarithmic expressionwrite the following logarithmic expression as a single logarithm with coefficient 1. log9 - 2logk?

Answer 1

The logarithmic expression log9 - 2logk can be expanded using the power rule and the quotient rule of logarithms to log(9/k^2).

Step-by-step explanation:

To expand the logarithmic expression log9 - 2logk as a single logarithm with coefficient 1, we can use the properties of logarithms. Specifically, we'll apply the power rule of logarithms, which says that log(a^n) = n * log(a).

First, we rewrite the term with the coefficient in front of the log:

• 2logk = log(k^2)

Now, we can combine the two logarithms into a single term by applying the quotient rule of logarithms, which states that log(a) - log(b) = log(a/b).

• log9 - log(k^2) = log(9/k^2)

Therefore, the expression log9 - 2logk can be written as log(9/k^2).