Question

Log ( 2 x 2 + 3x ) = log ( 6x + 2 )

Answer 1

Если логарифмы равны то равны и данные в скобках, т.е.

4+3x=6x+2

3x=2

Answer 2

To solve the equation log(2x^2 + 3x) = log(6x + 2), we can start by applying the logarithmic property that states if log(base a)(x) = log(base a)(y), then x = y.

Using this property, we can equate the expressions inside the logarithms:

2x^2 + 3x = 6x + 2

Rearranging the equation, we get:

2x^2 + 3x - 6x - 2 = 0

Simplifying:

2x^2 - 3x - 2 = 0

Now, we can solve this quadratic equation using factoring or the quadratic formula. Let's use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = -3, and c = -2. Substituting the values:

x = (-(-3) ± sqrt((-3)^2 - 4(2)(-2))) / (2(2)) x = (3 ± sqrt(9 + 16)) / 4 x = (3 ± sqrt(25)) / 4 x = (3 ± 5) / 4

Now, we have two possible solutions:

1. x = (3 + 5) / 4 = 8 / 4 = 2
2. x = (3 - 5) / 4 = -2 / 4 = -0.5

Therefore, the solutions to the equation log(2x^2 + 3x) = log(6x + 2) are x = 2 and x = -0.5.