Question

Lg(x^3)-lg(x+4)=lg(2x^2)-lg(2x-4)

Answer 1

Как видите в конце получил x1=4

и X2=-1

X2 не может быть решение так как если вы подставите обратно в уравнение -1 то у вас в логарифме будет отрицательное число что противоречит математике!

Answer 2

To solve the given equation, we can simplify the logarithmic expressions using logarithmic properties, and then solve for the variable x. Let's begin:

Using the logarithmic properties:

lg(x^3) - lg(x + 4) = lg(2x^2) - lg(2x - 4)

Applying the quotient rule of logarithms:

lg(x^3 / (x + 4)) = lg(2x^2 / (2x - 4))

Next, we can eliminate the logarithms by converting them into exponential form:

x^3 / (x + 4) = 2x^2 / (2x - 4)

Now, we can cross-multiply to get rid of the fractions:

(x^3)(2x - 4) = (2x^2)(x + 4)

Simplifying further:

2x^4 - 4x^3 = 2x^3 + 8x^2

Rearranging the terms:

2x^4 - 4x^3 - 2x^3 - 8x^2 = 0

Combining like terms:

2x^4 - 6x^3 - 8x^2 = 0

Factoring out 2x^2:

2x^2(x^2 - 3x - 4) = 0

Now, we can solve each factor separately:

1. 2x^2 = 0 x^2 = 0 x = 0

2. x^2 - 3x - 4 = 0 (x - 4)(x + 1) = 0

   Solving for x in each factor: x - 4 = 0 x = 4

   x + 1 = 0 x = -1

Therefore, the solutions to the equation lg(x^3) - lg(x + 4) = lg(2x^2) - lg(2x - 4) are x = 0, x = 4, and x = -1.