Question

Suppose that ln(3)=p. Use properties of logarithms to write ln(27) in terms of p.

Answer 1

ln(27) = 3p, utilizing the logarithmic property that allows expressing ln(
`a^b`) as b * ln(a). Given ln(3) = p, we substitute it into ln(27) = 3 * ln(3), simplifying to ln(27) = 3p.

Step-by-step explanation:

In the given question, we are provided with ln(3) = p. To find ln(27) in terms of p, we can use the property of logarithms that allows us to rewrite ln(
`a^b`) as b * ln(a). In this case, ln(27) can be expressed as ln(
`3^3`). Applying the logarithmic property, we get 3 * ln(3), and since ln(3) is given as p, the final answer is ln(27) = 3p.

Now, let's break down the steps. First, we recognize that 27 can be expressed as
`3^3`. Applying the logarithmic property, ln(27) becomes 3 * ln(3). Using the information provided, ln(3) = p, we substitute this into the expression, yielding ln(27) = 3p. This is the final answer to the question.

In essence, we've leveraged the logarithmic property to simplify ln(27) in terms of ln(3), which was given as p. This mathematical manipulation is a concise way to express ln(27) using the information provided in the question. The power of logarithmic properties lies in their ability to simplify complex expressions, providing a clear and straightforward solution to mathematical problems.

The complete question is:

"Suppose that ln(3) = p. Use properties of logarithms to express ln(27) in terms of p."