**Answer 1**

It is because f(x) = e^x and g(x) = ln x are inverse functions. This means that f(g(x)) = x

f(g(x)) = e^(lnx) = x.

Or you can think about how ln is defined.

ln x is defined to be the value y such that e^y = x

So if x = 7 and ln x = y

then substitution in e^y = x gives you.

e^(ln7) = 7

**Answer 2**

E Ln 7

**Answer 3**

Because if you take the ln of both sides, you get an equality.

e^ln7 = 7

LN BOTH SIDES:

ln(e^ln7) = ln7

when you take the natural log of e to something, the e goes away, so

ln7 = ln7

Since this equation is true, the one before also has to be true, because we just natural logged both sides–that doesn’t change the equality.

**Answer 4**

it doesn’t it equals 1.945910

ohh e^ln7 you mean?

haha because if e has a power of ln then it cancles the e such as e^ln(1)=1 e^ln59289455023 = 59289455023

**Answer 5**

The function ln(x) is the inverse of e^x and defined such that e^(ln(x)) = x.

**Answer 6**

__________________________

The definition of logarithm tells us:

ln(7) = a ⇐⇒ ℯª = 7 ← notice that a = ln(7)

ℯʵⁿ⁽⁷⁾ = 7 ← by substitution

___________________________

**Answer 7**

ln is base e.

so

e^ln(7)=7

The e’s cancel out

so all you’re left with 7=7.

Have a nice day

Source(s): Grade 10 math