Solve the equation ln(x+4)=2 for x. Give the exact answer?

Question

Solve the equation ln(x+4)=2 for x. Give the exact answer?

Answer 1

Hi,

Okay, to undo a natural log (ln), always remember that you raise it with base e which obviously is done to both sides to get:

e^(ln(x+4)) = e^2

Which simplifies to:

x + 4 = e^2

Now, we have to isolate for x alone by subtract 4 from both sides to get:

x = e^2 - 4 <=== FINAL ANSWER

I hope that helps you out!  Please let me know if you have any other questions!

Answer 2

x+4=2

     -4  -4 Subtract 4 from both sides of the equation

x = -2

Answer 3

ln(x+4)=2

lnx+ln4=2

ln(x*4) =2

ln4x    =2

x=2/ln4

  =1.442695041

  =1.44 (3 s.f)

Answer 4

ln is log x to the base e

so,

Log (x+4) to the base e = 2

by power rule, e^2 = x+4

=> x = e^2 - 4

=> x = (2.718)^2 - 4

=> x = 7.387524 - 4

Hence, x = 3.387534

Answer 5

x+4=2

x+4-4=2-4

x=-2