The base of a logarithm should always be positive and can't be equal to 1, so the domain is 0 < <em>x</em> < 1 or <em>x</em> > 1.
Write both sides as powers of 1/<em>x</em> :
Recall that , so that
Take the 5th root of both sides, recalling that 3⁵ = 243, so
Answer:
Step-by-step explanation:
-(4x+6)<2(5x+9)+2x
Distribute:
-4x-6<10x+18+2x
Combine like terms on either side:
-4x-6<12x+18
We want to now gather variable terms on one side of the inequality and constants (terms without variables) on the opposing side.
Add 4x on both sides:
-6<16x+18
Subtract 18 on both sides:
-24<16x
Divide both sides by 16:
-24/16<x
This implies:
x>-24/16
Reduce:
x>-3/2
x>-1.5
So in an interval notation this is .