Question

Log(2x+4)+log(x-2)=1

Answer 1

Ответ:

Пошаговое объяснение:

log(2x-4)(x-2)=log2(2)

2$x^{2}$-8x+8=2

Считаешь, корни 1 и 3

Answer 2

To solve the equation log(2x + 4) + log(x - 2) = 1, we can use logarithmic properties to simplify the equation and then solve for x.

First, we can apply the product rule of logarithms, which states that log(a) + log(b) = log(a * b). Therefore, we can rewrite the equation as a single logarithm:

log[(2x + 4)(x - 2)] = 1

Next, we can rewrite the equation in exponential form. The logarithmic equation log(base)(value) = exponent is equivalent to the exponential equation base^(exponent) = value. Applying this to our equation, we have:

(2x + 4)(x - 2) = 10^1

Simplifying further:

2x^2 - 4x + 4x - 8 = 10

Combining like terms:

2x^2 - 8 = 10

Rearranging the equation:

2x^2 = 18

Dividing both sides by 2:

x^2 = 9

Taking the square root of both sides:

x = ±3

So the solutions to the equation are x = 3 and x = -3.