Domain help Math 4 will pick Ba?

Question

thanks again. Here i have no idea on how to solve this

Rewrite as a single logarithm with a coefficient of one

(3ln(x))-(5ln(x))+ (1/2ln(x))

choices

ln(1/x^(5/2))

ln(x^(17/2)

ln(1/(x^(3/2))

ln(x)

ln(1/x^(15/2))

none of the above

Ty as i am clueless

Answer 1

First, go ahead and simplify this by adding like terms (in this case, all them then since they all have ln(x) in common) to get

(3 - 5 + 1/2)(ln(x)) = -(3/2)ln(x)

Now recall the property of logarithms which says you can bring a number out front of the log inside as an exponent of whatever is inside the log, i.e.

a ln(x) = ln(x^a)

So we have -(3/2)ln(x) = ln(x^(-3/2))

Which is the same thing as ln(1/(x^(3/2))).