Question

Lg(√x-√3)+lg(√x+√3)=2 одз

Answer 1

Свойства логарифмов, а точнее их сложение

Answer 2

To find the domain of the given logarithmic equation, we need to ensure that the argument of the logarithms is positive. In this case, we have:

lg(√x - √3) + lg(√x + √3) = 2

First, let's consider the individual arguments of the logarithms:

√x - √3 > 0

Solving for x:

√x > √3

x > 3

√x + √3 > 0

Solving for x:

√x > -√3

Since √x is always non-negative (i.e., it is always greater than or equal to 0), this condition is satisfied for all real values of x.

Now, we need to ensure that the argument of the first logarithm is positive:

√x - √3 > 0

x > 3

So, the domain of the given equation is all real numbers x greater than 3. In interval notation, it can be written as:

Domain: (3, +∞)