Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places.
-ln x + ln (x + 6)= 4
A) $- 6 + \sqrt { 36 + 4 \mathrm { e } ^ { 4 } } \approx 9.950$
B) $\frac { - 6 - \sqrt { 36 + 4 \mathrm { e } ^ { 4 } } } { 2 } \approx - 10.975$
C) $\frac { - 6 + \sqrt { 36 + 4 \mathrm { e } ^ { 4 } } } { 2 } \approx 4.975$
D) $\frac { - 6 + 2 \sqrt { 36 + \mathrm { e } ^ { 4 } } } { 2 } \approx 6.518$

Question

Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places.
-ln x + ln (x + 6)= 4 
A) $- 6 + \sqrt { 36 + 4 \mathrm { e } ^ { 4 } } \approx 9.950$
B) $\frac { - 6 - \sqrt { 36 + 4 \mathrm { e } ^ { 4 } } } { 2 } \approx - 10.975$
C) $\frac { - 6 + \sqrt { 36 + 4 \mathrm { e } ^ { 4 } } } { 2 } \approx 4.975$
D) $\frac { - 6 + 2 \sqrt { 36 + \mathrm { e } ^ { 4 } } } { 2 } \approx 6.518$

Quizplus · Accepted Answer

The equation can be rewritten as ln(x(x+6)) = 4, leading to x(x+6) = e^4. Solving the quadratic equation x^2 + 6x - e^4 = 0 gives the solution x = (-6 + sqrt(36 + 4e^4))/2.

Solve the Equation −6+36+4e4≈9.950- 6 + \sqrt { 36 + 4 \mathrm { e } ^ { 4 } } \approx 9.950−6+36+4e4​≈9.950

Solve the Equation $- 6 + \sqrt { 36 + 4 \mathrm { e } ^ { 4 } } \approx 9.950$