algebra 2 problem

Question

In x + In (x+4)=6  I need to simplify this with an exact solution

Answer 1

lnx + ln(x+4) = 6

 

ln[x(x+4)] = 6

 

x² + 4x = e⁶

 

x² + 4x - e⁶ = 0

 

x = [-4 ± √(16 + 4e⁶)]/2 = [-4 ± 2√(4 + e⁶)]/2

 

                                             = -2 ± √(4 + e⁶)

 

-2 - √(4 + e⁶) is extraneous because substituting this value for x in the original equation yields ln(negative number).  

 

solution:  -2  + √(4 + e⁶)