help with my precalc honors math Q???

Question

please help! and explain how Thanks!

Solve the logarithmic equation. Round the solution to three decimal places.

ln (sq root(x+1)) = 2

Answer 1

First thing you need to do is take e to the power of both sides.
e^ln u = u, no matter how complicated u is. This is also known as taking the antilog.
sqrt (x+1) = e^2
square both sides to get rid of the sqrt
(x+1) = (e^2)^2 = e^4
now subtract 1 from each side to get the x by itself.
x = e^4 - 1
Note: e^4 is a perfectly good number, even though it looks strange. Put it into the calculator for a decimal approximation ..
e^4 ~= 54.5981 and e^4 - 1 ~= 53.5981

Answer 2

1. exponentiatte both sides
e^ln(sqrt(x+1))=e^2
simplify:
sqrt(x+1)=e^2

2 square both sides

(sqrt(x+1))^2=(e^2)^2
simplify:
x+1=e^4

3. subtract 1 fm both sides to get

x=e^4-1