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

Examples
log10 100 = 2
10² = 100

log2 8 = 3
2³ = 8

Thus:-
loge (x + 3) = y
e^y = x + 3
x = e^y - 3

Answer 2

When we write ln x = y, it is natural logarithm of x = y. The base of natural logarithm is e. It means ln x is a number (=y) which when raised to e gives x, i.e., e^y = x

When obtaining inverse of y = ln (x + 3), first interchange the variable to get
ln (y + 3) = x and then by the same definition of log,
e^x = y + 3.

Answer 3

If you graph e^x you see and increasing positive function. The inverse function is called ln x.
So:
e^x: R->R+
and
ln x:R+->R
So if e^x=y the inverse goes back so ln y=x.
in your case replace y for y+3

Answer 4

f(x) = (2^x) / (a million + 2^x) enable y=(2^x) / (a million + 2^x) or y+y2^x =2^x or 2^x -y2^x = y or 2^x(a million-y) = y or 2^x = y/(a million-y) taking log of the two section log 2^x = log y/(a million-y) or xlog2 = log y/(a million-y) or x = a million/log2* log y/(a million-y) so inverse of the function f(x) =a million/log2* log x/(a million-x)

Answer 5

try this using your calculator

ln 20.085 = 2.999

e ^ 2.999 = e^(ln20.085) = 20.085

so it is the same with (y+3) e^(ln(y+3)) = y+3