Question

how do I write an equivalent exponential or logarithmic equation for the following:
e^x=55
In44=3.78
e^-3=0.05?

Answer 1

The natural log of a number means e to what power equals this number
\[\ln(e^2) = 2\]
This says e to what power is equal to e^2 which is obviously 2

\[e^a = b\]is the same thing as
\[\ln(b) = a\]

Answer 2

\[\boxed{\log_bx=y\quad\iff\quad x=b^y}\]\[\boxed{\quad\ln x=y\quad\iff\quad x=e^y}\]