I have the equation y = 15^x which determines the population and x is how many days.
Determine to the nearest day when the population will reach 600.
How do I figure out the above without just guess and check?
Even if your calculator does NOT have a logarithm, base 15, You can do $\displaystyle 600= 15^x$ using log base 10 (common log) [tex]log_{10} 600= log_{10}(15^x)= x log_{10}(15)[tex] so $\displaystyle x= \frac{log_{10}(600)}{log_{10}(15)}$.
Or with the natural logarithm key, "ln", $\displaystyle ln(600)= ln(15^x)= xln(15)$ so $\displaystyle x= \frac{ln(600)}{ln(15)}$.