Question

Express the given quantity as a single logarithm. (Enter your answer using function notation - use In(x) instead of in x.)

In(a+b)+In(ab)-4lnc

Answer 1

To express the given quantity as a single logarithm, we can use properties of logarithms to simplify the expression. The given quantity can be expressed as In(a^2b+ab^2)-ln(1/c^4).

Step-by-step explanation:

To express the given quantity as a single logarithm, we can use properties of logarithms to simplify the expression. Let's break it down step by step:

1. Using the property of logarithms, In(a+b) + In(ab) = In((a+b)(ab)).
2. Next, simplify In((a+b)(ab)) to In(a^2b+ab^2).
3. The last term, -4lnc, can be simplified by using the property of logarithms, lnc = -ln(1/c). So, -4lnc = -4ln(1/c) = -ln(1/c^4).
4. Now, combine the simplified terms to get In(a^2b+ab^2)-ln(1/c^4).

Therefore, the given quantity can be expressed as a single logarithm: In(a^2b+ab^2)-ln(1/c^4).