For which value of does the following inequality hold?
Hello,
If there is no mistake in the subject, i'll write this :
So you have to solve :
Differentiate the case when ln(x²-3) is positive (ie x²-3 > 1) and the case when ln(x²-3) is negative (ie x²-3 < 1).
Multiply the two sides with ln(x²-3), change the sign when it's negative.
Then, you may have ln(4x+2) > (or <) ln(x²-3), which is ln(4x+2) - ln(x²-3) > (or <) 0=ln(1)
<=> (or <)
Ln is an increasing function, so a<b <=> ln(a)<ln(b)
Hello, james_bond!
This one is trickier than I thought . . .
Solve for
We know that: . means: . (Think about it!)
So we have: .
This is a down-opening parabola which is positive between its x-intercepts.
Its x-intercepts are: (-1,0) and (5,0).
. . Hence, the inequality holds on the interval: .
But the base of a logarithm must be positive.
. . So we have: .
Moreover, the base of a logarithm cannot be 1.
. . So we have: .
Therefore: .