Question

Lg (x-1) + lg (x+1)= lg 3​

Answer 1

Ответ:

Итак, Lg a=log₁₀a

Далее,

lg(x-1)+lg(x+1)=3lg 2+lg(x-2) (3 lg 2=lg 2³=lg 8)

Св-ва логарифма: lg a+lg b=lg(a*b)

lg(x²-1)=lg(8x-16)

x²-1=8x-16

x²-1-8x+16=0

x²-8x+15=0

D=64-60=4

x₁=8+2/2=5

x₂=8-2/2=3

Т.к. у нас 2 полож. корня, необходимо надо найти ОДЗ логарифм. уравнения:

{x²-1>0

{8x-16>0

Ставим найденные иксы в неравенства:

{25-1>0

{40-16>0

{9-1>0

{24-16>0

Пошаговое объяснение:

Answer 2

To solve the equation lg(x - 1) + lg(x + 1) = lg(3), you can use the properties of logarithms. Here's how you can do it step by step:

1. Use the properties of logarithms to combine the two logarithms on the left side of the equation:

   lg((x - 1)(x + 1)) = lg(3)

2. Remove the common logarithm on both sides of the equation by taking the exponentials:

   (x - 1)(x + 1) = 3

3. Expand the left side of the equation by using the difference of squares formula:

   x^2 - 1 = 3

4. Add 1 to both sides to isolate x^2:

   x^2 = 4

5. Take the square root of both sides:

   x = ±2

So, the solutions to the equation are x = 2 and x = -2.