Question

Elsa tries to solve the following equation, and determines there is no solution. Is she correct? Explain.

Answer 1

The spot on correct answer for this is....

Identify the system of equations that can be graphed to solve the problem.

Use the change of base formula.

Determine that the graphs of the two equations do not intersect.

Determine that Elsa is correct; the equation has no solution.

Answer 2

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) in the opposite side. The equation will now be log2x-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 10^4=(2x/6x+10) and proceed in solving for x value which is equal to 1.667.