Question

Show that e^(-2ln5) = -25

Answer 1

I understand that -2ln(5) = ln (5^-2), but I'm stuck from here.

Answer 2

sorry, I mistyped the question.
"Show that e^(-2ln5) = 1/25"
not -25.

Answer 3

e^ ln (5^-2) = 5^-2 ( by definition)

Answer 4

5^-2 = 1/25

Answer 5

Why is e^ ln (5^-2) = 5^-2 ?

Answer 6

because ln = log to the base e

Answer 7

it might help to consider logs to the base 10

log _10 100 = 2 because 10^2 = 100
therefore, substituting 2 = log _10 100 in 10^2 = 100:
10 ^ (log_10 100) = 100