Find the value of x if ln e^x + ln e^3 = ln e^5

Given  lne^x+lne^3= lne^5.

We have
to determine x.

We know by definition of ln , the natural
logarithms, that

If e^a = b, then  a =
lnb.

Therfore ln e^a = c implies e^a = e^c implies a =c or a = ln
e^a.

So by definition ,  ln e^a =
a.

Therefore the given equation
becomes:

x+3 = 5.

Subtract
3:

x+3-3 = 5-3.

x =
2.

Therfore the solution of ln e^x+lne^3 = ln 5 is x =
2.