Question

Expand: In 2a³/b^4
In 2+3 In a -4 ln b
In 2-3 In a -4 lnb
In 2-3 In a + 4 lnb

Answer 1

The expression ln(2a^3/b^4) can be expanded using logarithmic properties to ln(2) + 3ln(a) - 4ln(b), which separates the numerator and the denominator and applies the power rule.

Step-by-step explanation:

The question asks us to expand the expression ln(2a3/b4) using the properties of logarithms. We will use the fact that ln(A/B) = ln(A) - ln(B) and ln(An) = nln(A).

Starting with the given expression:

ln(2a3/b4)

Using the property of logarithms that deals with division, we can separate the numerator and the denominator:

ln(2a3) - ln(b4)

Now, we separate the coefficient from the variable in the log of the numerator and use the power rule for logarithms:

ln(2) + ln(a3) - ln(b4)

Apply the power rule for logarithms:

ln(2) + 3ln(a) - 4ln(b)

Therefore, the expanded form of the original expression ln(2a3/b4) is ln(2) + 3ln(a) - 4ln(b).