y = e^(2*ln(3)); y =?

Question

I need help understanding how to find the exact value of y. I see in the back of book the answer is 9, but don't understand *how* this is calculated.

Answer 1

Solve for y.

y = e^[2*ln(3)] = e^[ln(3²)] = 3² = 9

Answer 2

Use the property of logs to write 2*ln(3) = ln(3^2) = ln(9)
(the coefficient becomes the exponent )
Then use the fact that ln x and e^x are inverse functions:
e^(2*ln(3)) = e^(ln(3^2)) = e^(ln(9)) = 9

Answer 3

Rewrite it as

y = (e^ln(3))^2
(this uses the rule of exponents: b^cd = (b^c)^d)

But e^ln(a) = a for any a, so

this just becomes

y = 3^2 = 9

Answer 4

step 1, replace 2*ln(3) to ln(3)^2 (power property):
y = e^(ln(3)^2)

step 2, replace e^(ln(3)^2) to 3^2 because e^ln = 1:
y = 3^2

step 3, solve:
y = 9

Answer 5

Scientific calculator :

1) 3
2) ln
3) x
4) 2
5) =
6) eˣ

Answer 6

y = e^(2*ln(3)) = e^(ln(3^2))=e^(ln(9))=9