Posted by **elley** on Thursday, November 6, 2008 at 8:22pm.

show that the solution has exactly one solution in the interval

x+ln(x+1)=0, 0<and equal to x <and equal to 3

- Calculas HS -
**Reiny**, Thursday, November 6, 2008 at 8:36pm
x+ln(x+1)=0 , 0 ≤ x ≤ 3

write your equation as ln(x+1) = -x

now let the left side by

y = ln(x+1) and the right side

y = -x

and make a quick sketch of each on the same x-y plane.

the first one is the log function crossing the x axis at the origin, slowing rising in the first quadrant, and dropping down into the third quadrant.

the other graph is a straigh line with slope of -1 and passing through the origin.

Clearly they can only cross at x=0, which becomes your only answer.

check : if x=0

LS = 0 + ln(0+1)

= 0 + 0 = 0 = RS

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