# Thread: Exponential and logarithmic Functions help

1. ## Exponential and logarithmic Functions help

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?

2. You can set $\displaystyle y=600$ and take logarithms on both side to solve for $\displaystyle x$.

3. Originally Posted by olen12
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?
guess and check will work fine unless your calculator can calculate base 15, then...

$\displaystyle x= log_{15}(600)$

4. Originally Posted by pickslides
guess and check will work fine unless your calculator can calculate base 15, then...

$\displaystyle x= log_{15}(600)$
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 $\displaystyle x= \frac{ln(600)}{ln(15)}$.