Question

Suppose that ln2=s. Use properties of logarithms to write the logarithm in terms of s. In 8

Answer 1

To write the logarithm in terms of s, we can use properties of logarithms. Using the properties that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers, and the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers, we can rewrite ln(8) as 3s.

Step-by-step explanation:

To write the logarithm in terms of s, we can rewrite the logarithmic expression using properties of logarithms. The properties that we can use are:

1. The logarithm of a product of two numbers is the sum of the logarithms of the two numbers: ln(xy) = ln(x) + ln(y).
2. The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers: ln(x/y) = ln(x) - ln(y).

Now, let's write the logarithm in terms of s for ln(8):

ln(8) = ln(2 * 2 * 2) = ln(2) + ln(2) + ln(2) = s + s + s = 3s.