Solve the equation. log_(2)(3x-2)-log_(2)(x-5)=4 A. 18 B. (3)/(13) C. (38)/(5) D. 6

## Step 1: Combining the Logarithms<br />### Using the quotient rule of logarithms, which states $log_b(m) - log_b(n) = log_b(\frac{m}{n})$, we can combine the two logarithms on the left side of the equation. This simplifies the equation to a single logarithm.<br />## Step 2: Converting to Exponential Form<br />### We convert the logarithmic equation to its equivalent exponential form. The base of the logarithm becomes the base of the exponent, the right side becomes the exponent, and the argument of the logarithm becomes the result. This gives us an equation without logarithms.<br />## Step 3: Solving for x<br />### Now we have a simple algebraic equation. We multiply both sides by $(x-5)$ to eliminate the fraction, then distribute and isolate $x$ to solve for its value.<br />## Step 4: Checking for Extraneous Solutions<br />### We must check if the solution is valid by plugging it back into the original logarithmic equation. The argument of a logarithm must be positive. If the solution makes any argument non-positive, it is extraneous and must be discarded.