For the inverse function, the output becomes the input. thus, to find the inverse function, we switch the output and input, and solve for the new input (which is the old output).

Let

Thus we have

For :

........now we solve for

Take log to the base 2 of both sides, we obtain

as desired

...not much thinking required there. remember what the definition of a logarithm is, i've stated it several times on this forum, do a search for it if you wish. for the sake of completeness we will show it more explicitly

2. Find log2(8).

Let

Equating coefficients we get:

after 3 hours we have 8 million bacteria.What does your result mean in terms of the bacterium?

do you see why?