Write the expression below as a single logarithm. Please show all of your work.

Question

Answer 1

2 ln(x+ 4) -ln{(x^2 + x - 12)/x}

Formula : a ln(x) = ln(x)^a 

= ln(x + 4)^2 - ln{(x^2 + x - 12)/x}

multiple value form : ln(a) - ln(b) = ln(a/b)

= ln[(x+4)^2 /{(x^2 + x - 12)/x}]

= ln[(x(x+4)^2) /(x^2 + x - 12)]

Formula :(a + b)^2 = a^2 +2ab +b^2

= ln[(x(x^2 + 8x +16) /(x^2 + x - 12)]

= ln[(x^3 +8x^2 +16x) /(x^2 + x - 12)]

The solution is = ln[(x^3 +8x^2 +16x) /(x^2 + x - 12)]