Question

bonnie and emily tried to solve the following logarithmic equation and found different solutions.\\(\log_{5}(-3x + 7) = 0\\)\\(\bullet) bonnie states that there is no solution.\\(\bullet) emily states the solution is \\(x = 2\\).\
who is correct and why?\
choose 1 answer:\
\\(\bigcirc\\) a bonnie is correct as the value \\(x = 2\\) creates a negative argument in \\(\log_{5}(-3x + 7)\\).\
\\(\bigcirc\\) b emily is correct as she solves the equation by converting it to an exponential.\
\\(\bigcirc\\) c neither are correct as the solution to the equation is \\(x = \frac{2}{3}\\).

Explanation:

Step1: Convert log to exponential form

$$5^0 = -3x + 7$$

Step2: Simplify exponential term

$$1 = -3x + 7$$

Step3: Solve for x

$$-3x = 1 - 7 = -6 \implies x = \frac{-6}{-3} = 2$$

Step4: Check log argument validity

$$-3(2) + 7 = -6 + 7 = 1$$

Answer:

B. Emily is correct as she solves the equation by converting it to an exponential.