Question

Elsa tries to solve the following equation, and determines there is no solution. Is she correct? Explain. log2x = log2(3x + 5) + 4

Answer 1

Given: The equation  log2x = log2(3x + 5) + 4

To find: Whether the equation has any solution or not?

Solution:

• We have provided with logarithmic equation:  log 2x = log 2(3x + 5) + 4

• Now taking logarithmic terms on one side, we get:

             log 2x - log 2(3x + 5) = 4

• Now we know the identity: log a - log b = log(a/b)

             log (2x / 2(3x+5)) = 4

             log (x / 3x+5) = 4

• Now converting it into base form, we get:

             x / 3x+5 = 10^4

             x = 10^4 x 3x + 5 x 10^4

             x - 30000x = 50000

             -29999x = 50000

             x = -50000/29999

             x = -1.6667

Answer:

          So elsa is wrong. There is a solution for the equation log2x = log2(3x + 5) + 4 which is x = -1.6667 .

Answer 2

Answer:

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.

Step-by-step explanation:

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