Question

Lg(2x-1)+lg(x+5)=lg13

Answer 1

Ответ:

lg(2x-1)+lg(x+5)=lg13

2x-1+x+5=13

2x-1+x+5-13=0

3x-9=0

3x=9

x=3

Объяснение:

Answer 2

To solve the equation lg(2x-1) + lg(x+5) = lg(13), we can use logarithmic properties to simplify the equation.

First, let's apply the product rule of logarithms, which states that log(a) + log(b) = log(a * b):

lg(2x-1) + lg(x+5) = lg(13)

Using the product rule, we can combine the logarithms on the left side of the equation:

lg((2x-1) * (x+5)) = lg(13)

Next, we can remove the logarithms by applying the exponential function to both sides of the equation. The exponential function is the inverse of the logarithmic function:

(2x-1) * (x+5) = 13

Now, we have a quadratic equation. Let's expand and simplify:

2x^2 + 9x - 6 = 13

Rearranging the equation to bring everything to one side:

2x^2 + 9x - 19 = 0

At this point, we can solve this quadratic equation using factoring, completing the square, or using the quadratic formula. However, in this case, the quadratic equation does not factor easily, so let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = 9, and c = -19. Substituting these values into the quadratic formula:

x = (-9 ± √(9^2 - 4 * 2 * -19)) / (2 * 2)

Simplifying further:

x = (-9 ± √(81 + 152)) / 4 x = (-9 ± √233) / 4

Therefore, the solutions to the equation lg(2x-1) + lg(x+5) = lg(13) are:

x = (-9 + √233) / 4 x = (-9 - √233) / 4