Question 227801
So you have been given A and have been asked to find t:
{{{250 = 60log((250t+1))}}}
We need to "peel away" everything but the "t" on the right side. We can start with the 60 by dividing both sides by 60:
{{{25/6 = log((250t+1))}}}
There are a couple of ways to proceed from here:<ul><li>If your calculator has a button for the <i>inverse</i> log function (it <i>may</i> look like "log" with an exponent of -1) and you know how to use it:<ol><li>Use it on 25/6. (The correct number is between 10,000 and 100,000. If you don't get this, then abandon this procedure.)</li><li>Write an equation that says the number you get from the previous step equals 250t+1</li></ol></li></ol></li><li>Without an inverse log key or without the knowledge of how to use it correctly:<ol><li>Rewrite the equation in exponential form. The basic pattern is: {{{x = log(b, (y))}}} means the same as {{{b^x = y}}}. Using this on our equation we get (since the base of "log" is 10):
{{{10^(25/6) = 250t+1}}}</li><li>Now we need our calculator to raise 10 to the 25/6 power. Different calculators have different buttons for this. Often it looks like "^" or "{{{x^y}}}". We should get 14578 (approximately). Put this number into our equation</li></ol></li></ul>
Either way we should now have an equation like:
{{{14678 = 250t + 1}}}
Solve this equation. Subtract 1 from each side:
{{{14677 = 250t}}}
Divide both sides by 250:
{{{58.7 = t}}}
Remembering that approximations and rounding were used no matter how we solved this, our answer is: After approximately 58.7 hours 250 hectares will be burned.