Solve log(base4)X + log(base4) (X+6) <2

[VVVS]

Homework Statement

Solve log(base4)X + log(base4) (X+6) <2

Homework Equations

log(base4)X + log(base4) (X+6) =2 comes out to x=-8 and X=2

The Attempt at a Solution

I can't seem to figure out what steps I should even take to answer this inequality.

 

[rahl___]

this property should be useful:
$$log_a (b*c) = log_a b + log_a c$$
applying this to your inequality and changing 2 into $$log_4 16$$ you'll get something that can be easily transferred into inequality containing quadratic function, which you'll surely solve on your own

 

[Mark44]

Homework Statement

Solve log(base4)X + log(base4) (X+6) <2

Homework Equations

log(base4)X + log(base4) (X+6) =2 comes out to x=-8 and X=2

One relevant equation here would be log_aA + log_aB = log_aAB.
Another is log_ab = c <==> b = a^c.
The equation you have here is part of your work, not really a relevant equation.

The Attempt at a Solution

I can't seem to figure out what steps I should even take to answer this inequality.

First off, you should determine which values of x are going to be allowed as potential solutions. Then, see if the equations I added might be of some help to you.