Log5(3x+1)>log5(x-3) промежуток

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вопрос

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, ∞).