Question

Which of the following shows the true solution to the logarithmic equation below? log(x)+log(x+5)=log(6x+12)

a. x=−8
b. y=4
c. x=−3 and x=4
d. x=−3 and x=−4

Answer 1

To solve the logarithmic equation, combine the logarithms on the left side of the equation using the property log(a) + log(b) = log(ab). Simplify the resulting equation and find the solutions using factoring or the quadratic formula. The true solution to the logarithmic equation is x = -3 and x = 4.

Step-by-step explanation:

To solve the logarithmic equation, you can combine the logarithms on the left side of the equation using the property log(a) + log(b) = log(ab).

Applying this property, the equation becomes log(x*(x+5)) = log(6x+12).

Since the logarithms are equal, the quantities inside the logarithms must also be equal, so x*(x+5) = 6x+12.

Expanding and rearranging the equation, we get
`x^2 + 5x - 6x - 12 = 0`.

Simplifying further, we have
`x^2 - x - 12 = 0`

Factoring or using the quadratic formula, we find the solutions to be x = -3 and x = 4.

Therefore, the true solution to the logarithmic equation is x = -3 and x = 4.