Question

Write ln(a^2 b^3/cd) in expanded form.

a) ln(a^2) + ln(b^3) - ln(cd)

b) 2ln(a) + 3ln(b) - ln(c) - ln(d)

c) ln(a^2) + ln(b^3) + ln(c) - ln(d)

d) ln(a^2) - ln(b^3) - ln(c) + ln(d)

Answer 1

To expand ln(a^2 b^3/cd), we apply logarithmic properties to get the final form: 2ln(a) + 3ln(b) - ln(c) - ln(d), which matches option b.

Step-by-step explanation:

To write ln(a^2 b^3/cd) in expanded form, we will use the properties of logarithms. The logarithm of a product of numbers is the sum of the logarithms, and the logarithm of a division is the difference of the logarithms. Furthermore, the logarithm of a number raised to a power is the power times the logarithm of the number.

Applying these rules:

• ln(a^2 b^3/cd) becomes ln(a^2) + ln(b^3) - ln(cd)
• We can further expand this to 2ln(a) + 3ln(b) - (ln(c) + ln(d)) using the power rule
• This simplifies to the final expanded form: 2ln(a) + 3ln(b) - ln(c) - ln(d)