To determine the interval where the inequality Log5(3x+1)>log5(x-3) is true, we first need to isolate x by getting rid of the logarithm.
Using the property if log_a(b) > log_a(c) then b > c. We can rewrite the inequality as 3x+1 > x-3.
Now, solve for x:3x + 1 > x - 33x - x > -3 - 12x > -4x > -2
Therefore, the solution for the inequality is x > -2.
The interval where the inequality Log5(3x+1)>log5(x-3) is true is (-2, ∞).
To determine the interval where the inequality Log5(3x+1)>log5(x-3) is true, we first need to isolate x by getting rid of the logarithm.
Using the property if log_a(b) > log_a(c) then b > c. We can rewrite the inequality as 3x+1 > x-3.
Now, solve for x:
3x + 1 > x - 3
3x - x > -3 - 1
2x > -4
x > -2
Therefore, the solution for the inequality is x > -2.
The interval where the inequality Log5(3x+1)>log5(x-3) is true is (-2, ∞).