# Math Help - Domain of e function

1. ## Domain of e function

How do I find the domain of
$
y=\sqrt{e^{5x}-2}
$

I have a test in a few hours so thanks for any help I can get!

2. Can you have negatives inside a radical?

What values of x cause the argument of the radical to be zero or greater?

How do I find the domain of: . $
y\:=\:\sqrt{e^{5x}-2}$

. . $e^{5x} - 2 \:\geq \:0$

. . . . . $e^{5x} \:\geq \:2$

. . . . . $5x \:\geq \:\ln 2$

. . . . . $x \:\geq \:\tfrac{1}{5}\ln2$

4. Thank you!

Here is another one:

$log_{4}+log_{4}(3x+11)=1$
$x(3x+11)=4$
$3x^{2}+11x-4=0$
I get x=1 and x=-11

The q is to find all solutions
Is this correct, or did I go wrong?

Thank you!

Here is another one:

$log_{4}+log_{4}(3x+11)=1$
$x(3x+11)=4$
$3x^{2}+11x-4=0$
I get x=1 and x=-11

The q is to find all solutions
Is this correct, or did I go wrong?
You didn't solve the quadratic correctly - use the quadratic formula to solve.

Also log terms must be greater than 0 so the domain is $x > -\frac{11}{3}$

6. Yes I was thinking I should have used the quad formula....thank you so much

$log_{4}+log_{4}(3x+11)=1$