SOLUTION: find the domain of the following function in interval notation : f(x)= 3&#8730;ln(x/2)

Click here to see ALL problems on logarithm

Question 639079: find the domain of the following function in interval notation :
f(x)= 3√ln(x/2)

Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
First of all, the argument of any logarithm must be positive. So

which resolves to

Second, the radicand of a square root must not be negative. So:

You might be able to logically dtermine from this that

After all, an exponent of 0 results in 1. So any argument of 1 or greater will have an exponent greater than 0. If you can't see this then we have to solve . We solve the inequality by rewriting it in exponential form:

Since any non-zero number, including e, to the zero power is 1 this becomes:

Multiplying by 2 we get:

From the fact that the argument of the log had to be positive we found that

must be true. From the fact that radicands of square roots must bot be negative we found that

must be true. Since both of these must be true, the domain must be

(since any number greater than or equal to 2 must also be greater than 0).

SOLUTION: find the domain of the following function in interval notation : f(x)= 3&#8730;ln(x/2)

SOLUTION: find the domain of the following function in interval notation : f(x)= 3√ln(x/2)