logarithm inverse function question?

Question

y = 1n (x+3)
x = 1n (y +3)
e^x = y + 3 <--- this is the part i dont understand
e^x - 3 = y

like what rule or defintion allows this step. how come when you put e^x, the 1n disappears? help please, im so confused. i want to understand.

Answer 1

note that , ln(e^x) = x ln (e) , ln (e) = 1, so ,

e^x = y+3
then , e^x/(y+3) = 1 ,

x-ln(y+3) = 0 ,
x = ln(y+3)

as simple as that

Answer 2

if you have a natural log that you want to get rid of, you can raise e to the power of the ln (both sides) and then the e and ln cancel out.

Answer 3

Because ln and e^ are inverse fn

ln(e^x) = x and e^(ln x) = x

if y = e^x ln y = x
and y = ln x e^y = x