The situation reads as follows:
There are 3000 barbs in a pond and every year 20% of the barbs die and then 1000 new barbs come to the pond. A logarithmic function needs to be plotted to graph this change in population.
I worked through a part of the above situation and arrived at the function: $$ y = 3000(0.8^x) + 1000(0.8^{x-1}) + 0.8^{x-2} + \dotsb + 0.8^1 + 0.8^0 $$
How do I convert this above equation into a logarithmic function?
If you work out the numbers for about $30$ years you will see that the values get closer and closer to $5000$ from below without reaching it. Another way to find the special value $5000$ is to ask which value of $y$ will cause no change in the population the next year. This gives the equation $y=0.8y+1000$ which has the solution $y=5000$.
So if you consider the "base line" to be $5000$ you can reword the expression as:
This leads to the formula
$$y=5000-2000\cdot 0.8^x$$
Note, however, that this is an exponential expression, not a logarithmic one. You do get a logarithm if you solve for $x$, namely
$$x=\log_{0.8}\frac{5000-y}{2000}$$
or perhaps
$$x=\frac{\ln(5000-y)-\ln 2000}{\ln 0.8}$$