Question

solve the equation:
ln square root (x+7)=4
please show me step by step:)... thanks

Answer 1

\[\sqrt{x+7}=4\]?

Answer 2

squaring both sides, we get
x+7 = 16
x = 16-7
x = 9

Answer 3

square both sides so you get
+/-(x+7)=16
then solve for both cases:

case one
x+7=16
x=9

case two:
-(x+7)=16
x+7=-16
x=-23

check for extraneous solutions and we find that if x=-23 we will get sqareroot of a negative so x cannot be -23 thus
x=9

Answer 4

\[ln \sqrt{x+7}=4\]

Answer 5

natural log??

Answer 6

dang... lol ok
so then if you rewrite the natural log in exponenital form you get:
sqrt(x+7)=e^4
then square both sides so
x+7=e^8
x=(e^8)-7

Answer 7

there is the negative case senario which would work as well where:

-(x+7)=e^8
so
x+7=-(e^8)
thus
x=(-(e^8))-7

Answer 8

but that would give you an unreal answer which is not an option

Answer 9

\[\frac{1}{2}\ln(x+7)=4\]\[\ln(x+7)=4*\frac{2}{1}\]\[\ln(x+7)=8\]\[x=e^8-7\]