why does e to the ln7 = 7?

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

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