if x=e^t what is t how do you find it.?

Question

I know that if x=-t then multiply both sides by -1.
In this problem I am thinking you multiply both side by (ln) the natural log to eliminate the e and the answer is t= ln(x).

Answer 1

Ln is a function (an Unary operator.)
it cannot be multiplied.
Ln is natural LOG i.e. log with base 'e'


for x=e^t,
is multiplied with a number(scalar) ,say 2 it will become
2x=2e^t

but by taking ln on both sides we get:
L.H.S=ln(x)
r.h.s=ln(e^t)

=t*ln(e) in this step the power of 'e' comes down as an index.

=t as ln(e)=1.

for better details refer to LOGARITHM chapters in text

Answer 2

If my memory is correct ....

log x = t * log e
therefore

t = log x/log e

Answer 3

x=e^t
LN(x)=LN(e^t )=tLN(e)=t(1)=t

Answer 4

What you think is what's correct.