Question

Lg 5x + lg (x-1)= 1​

Answer 1

Пошаговое объяснение:

lg 5x + lg (x-1) = lg 10

lg (5x²-5x) = lg 10

5x² - 5x = 10

5x²- 5x - 10 = 0 , делим на 5

x² - x - 2 = 0

x1 + x2 = 1

x1 * x2 = -2

x1 = 2

x2 = -1   (не подходит)

ОДЗ : x-1 > 0           x>1

Ответ : x = 2

Answer 2

To solve the equation lg(5x) + lg(x - 1) = 1, we can simplify it using logarithmic properties and then solve for x.

First, we'll use the logarithmic property that states: log(a) + log(b) = log(a * b).

Therefore, we can rewrite the equation as follows:

lg(5x(x - 1)) = 1.

Next, we'll rewrite the equation in exponential form:

10^1 = 5x(x - 1).

This simplifies to:

10 = 5x^2 - 5x.

Rearranging the equation:

5x^2 - 5x - 10 = 0.

Divide the entire equation by 5 to simplify further:

x^2 - x - 2 = 0.

Now we can factor the quadratic equation:

(x - 2)(x + 1) = 0.

Setting each factor equal to zero:

x - 2 = 0 or x + 1 = 0.

Solving for x:

x = 2 or x = -1.

Therefore, the solutions to the equation are x = 2 and x = -1.