Question

Solve the following logarithmic equation: log7x log7(3x-2) = 0

a. x=1
b. x=2
c. x=3
d. x=4

Answer 1

To solve the logarithmic equation log7x log7(3x-2) = 0, we can use the property of logarithms. Setting both log7x and log7(3x-2) equal to 1, we solve for x and find x = 7. Then, setting log7(3x-2) equal to 1 and solving for x, we find x = 3. Therefore, the solutions to the equation are x = 7 and x = 3.

Step-by-step explanation:

To solve the logarithmic equation: log7x log7(3x-2) = 0

1. Apply the property of logarithms that states loga(b) = 0 if and only if b = 1. Therefore, set both log7x and log7(3x-2) equal to 1.
2. Set log7x = 1 and solve for x. Since the base is 7, the logarithmic equation can be written as 71 = x, which simplifies to x = 7.
3. Set log7(3x-2) = 1 and solve for x. Rewrite the equation as 71 = 3x-2 and solve for x. Add 2 to both sides of the equation to isolate the variable x. 7 + 2 = 3x, which simplifies to 9 = 3x. Divide both sides of the equation by 3 to solve for x. x = 3.

Therefore, the solutions to the logarithmic equation are x = 7 and x = 3. So, the correct option is c. x = 3.