Use the properties of logarithms to solve.
-
B) 7

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can simplify the left side of the equation as follows:

log(base 3)(x+1) + log(base 3)(2x-1) - log(base 3)2 = log(base 3)(3x)

log(base 3)((x+1)(2x-1)/2) = log(base 3)(3x)

(x+1)(2x-1)/2 = 3x

Expanding and simplifying, we get:

2x^2 - 5x + 2 = 0

Solving for x using the quadratic formula, we get:

x = 1/2 or x = 2

But we need to check our solutions to ensure that they are valid in the original equation. Plugging in x = 1/2, we get:

log(base 3)(3/2) + log(base 3)(0) - log(base 3)2 = log(base 3)(3/2)

The second term is undefined, so x = 1/2 is not a valid solution.

Plugging in x = 2, we get:

log(base 3)(3) + log(base 3)(3) - log(base 3)2 = log(base 3)(6)

This is a valid solution, so the answer is C, x = 2.

Use the Properties of Logarithms to Solve