Question

Elsa's answer is incorrect since there is a solution of the given equation. In the given logarithmic problem, we need to simplify the problem by transposing log2(3x + 5) to the opposite side. The equation will now be log2(x) - log2(3x + 5) = 4. Using properties of logarithm, we further simplify the problem into a new form log(2x/6x + 10) = 4. Then transform the equation into base form 10⁴ = (2x/6x + 10) and proceed in solving for the value of x, which is equal to 1.667.

Answer 1

The student's method of solving the logarithmic equation is incorrect. Using the property of logarithms correctly, we combine the logs into a single expression and solve for x.

Step-by-step explanation:

The student's approach to solving the logarithmic equation is not correct. The correct step is to use the property of logarithms which states that the logarithm of a quotient is the difference of the logarithms: logb(x/y) = logb(x) - logb(y). In the equation log2(x) - log2(3x + 5) = 4, we apply this property to combine the logarithms into a single logarithm, yielding log2(x/(3x + 5)) = 4. We then exponentiate with 2 as the base to obtain 24 = x/(3x + 5), leading to 16(3x + 5) = x, which can be solved for x.

To correct the student's solution, we do not convert to base 10 nor simplify to (2x/6x + 10). Their final answer could also not possibly be 1.667, as that does not satisfy the original equation. A systematic approach using properties of logarithms should lead to the correct solution.