Question

Lg(2x-3)>Lg(x+1)

Answer 1

Lg(2x-3)>Lg(x+1)          {2x-3>0       {2x>3     {x>1,5

2x-3>x+1                    {x+1>0        {x>-1      {x>-1       x>1,5 - ОДЗ

2x-x>3+1

x>4 входит в ОДЗ

Ответ: (4;+бесконечность)

Answer 2

I can help you with math problems and other topics. You asked me to solve the logarithmic inequality lg(2x-3) > lg(x+1). Here is the solution:

First, we can use the property of logarithms that lg(a) > lg(b) if and only if a > b. So, we can rewrite the inequality as 2x-3 > x+1.

Next, we can simplify the inequality by subtracting x from both sides and adding 3 to both sides. This gives us x > 4.

Finally, we can check the solution by plugging in a value of x that is greater than 4, such as x = 5. We get lg(2*5-3) > lg(5+1), which is true. Therefore, the solution is correct.

The answer is x > 4. You can also use online calculators to check your work or get more steps. For example, you can try [this one](https://www.mathway.com/Calculator/logarithm-calculator) or [this one](https://mathsolver.microsoft.com/en/solve-problem/%60lg%20x%20%2B%20%60lg%202%20-%20%60lg%20%28%20x%20-%202%20%29%20%3D%20%60lg%203). I hope this helps.