Question

Why is ln(e^-2) = -2.
Why doesn't it = e^-2??

Answer 1

ln (e^x) = x ln e = x * 1 = x

Answer 2

so what if it was ln5(e^-2). would the answer be -10?? thanks for your help:)

Answer 3

No, it is only because ln is base e that ln(e^x) = x

in general
loga (a^x) = x loga(a) = x*1 = x

log 5 of 5 is 1, but log5 (e) is not one

Answer 4

okay thanks

Answer 5

it is all because
b^logb (x) = x
so
5^log5 (5) = 5
so log5 (5) has to be 1

Answer 6

thanks damon!!!!!!