Question

What’s the value of c in the equation log(3c + 4) – log(c-6) = log(c+6)?

a) c = 5
b) c = 6
c) c = 7
d) c = 8

Answer 1

To find the value of c in the equation log(3c + 4) – log(c-6) = log(c+6), we can simplify the equation using logarithmic properties and then solve for c. The value of c is 8 (option d).

Step-by-step explanation:

To find the value of c in the equation log(3c + 4) – log(c-6) = log(c+6), we can simplify the equation using logarithmic properties. The property states that log(a) - log(b) = log(a/b). So, we can rewrite the equation as log((3c + 4)/(c-6)) = log(c+6). Since the logarithms are equal, we can equate the expressions inside the logarithms, (3c + 4)/(c-6) = c+6. Now, we can solve for c by cross-multiplying and simplifying the equation.

1. Multiply both sides of the equation by (c-6) to get (3c + 4) = (c+6)(c-6).
2. Distribute on the right side to obtain (3c + 4) = c^2 - 36.
3. Rearrange the equation to form a quadratic equation: c^2 - 3c - 32 = 0.
4. Factor or use the quadratic formula to solve for c. The solutions are c = -4 and c = 8.

So, the value of c in the equation is c = 8 (option d).