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

Edge 2020:

Explanation:

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

Yes, Elsa is correct.

Explanation:

The given equation is

`\log_2x=\log_2(3x+5)+4`

Elsa tries to solve the equation, and determines there is no solution. We need to check whether she is correct or not.

The given equation can be rewritten as

`\log_2x=\log_2(3x+5)+\log_22^4`
`[\because \log_aa^x=x]`

`\log_2x=\log_2(3x+5)+\log_216`

`\log_2x=\log_2[(3x+5)16]`
`[\because \log mn=\log m+\log n]`

`\log_2x=\log_2(48x+80)`

On comparing both sides, we get

`x=48x+80`

`x-48x=80`

`-47x=80`

`x=-(80)/(47)`

The value of x can not be negative because log is not defined for negative values.

Therefore, Elsa is correct and given equation have no solution.