To solve this inequality, we need to isolate the logarithmic term first.
First, divide both sides by 3:
log1/3 (x^2+2x) > -1/3
Next, we need to get rid of the logarithm by rewriting it as an exponential equation:
10^(-1/3) < x^2 + 2x
Now, simplify the left side by taking the cube root of 10:
0.46416 < x^2 + 2x
Subtracting 0.46416 from both sides gives:
0 < x^2 + 2x - 0.46416
Now, we need to solve for x by factoring the quadratic equation:
0 = (x + 2.154)(x - 2.154)
So, x is in the range of (-2.154, 0) U (0, 2.154).
To solve this inequality, we need to isolate the logarithmic term first.
First, divide both sides by 3:
log1/3 (x^2+2x) > -1/3
Next, we need to get rid of the logarithm by rewriting it as an exponential equation:
10^(-1/3) < x^2 + 2x
Now, simplify the left side by taking the cube root of 10:
0.46416 < x^2 + 2x
Subtracting 0.46416 from both sides gives:
0 < x^2 + 2x - 0.46416
Now, we need to solve for x by factoring the quadratic equation:
0 = (x + 2.154)(x - 2.154)
So, x is in the range of (-2.154, 0) U (0, 2.154).