Rewrite the expression

Question

as a single logarithm  .

Then the function 

Answer 1

A number in front of a logarithm can be brought inside as an exponent:

3ln(a - b) = ln(a - b)³

4ln(c) = ln(c⁴)

Two logarithms with the same base that are being added are the same as a single logarithm with the numbers multiplied and two logarithms with the same base that are being subtracted are the same as a single logarithm with the numbers being divided:

ln(a + b) + ln(a - b)³ - ln(c⁴) = ln[(a + b)(a - b)³/c⁴] and that's as simple as it gets so

A = (a + b)(a - b)³/c⁴