SOLUTION: HEY could you please help me answer this question? the land area in hectres (A) destroyed by a bushfire (t) hours after it started is expressed by A = 60log(250t+1) how lon

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: HEY could you please help me answer this question? the land area in hectres (A) destroyed by a bushfire (t) hours after it started is expressed by A = 60log(250t+1) how lon      Log On


   

Question 227801: HEY could you please help me answer this question?
the land area in hectres (A) destroyed by a bushfire (t) hours after it started is expressed by
A = 60log(250t+1)
how long does it take to burn out 250 hectares?
thank you
viki
Found 2 solutions by jsmallt9, nerdybill:
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
So you have been given A and have been asked to find t:
250+=+60log%28%28250t%2B1%29%29
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%2F6+=+log%28%28250t%2B1%29%29
There are a couple of ways to proceed from here:
  • If your calculator has a button for the inverse log function (it may look like "log" with an exponent of -1) and you know how to use it:
    1. 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.)
    2. Write an equation that says the number you get from the previous step equals 250t+1
  • Without an inverse log key or without the knowledge of how to use it correctly:
    1. Rewrite the equation in exponential form. The basic pattern is: x+=+log%28b%2C+%28y%29%29 means the same as b%5Ex+=+y. Using this on our equation we get (since the base of "log" is 10):
      10%5E%2825%2F6%29+=+250t%2B1
    2. 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%5Ey". We should get 14578 (approximately). Put this number into our equation

Either way we should now have an equation like:
14678+=+250t+%2B+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.

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Since you were given:
A = 60log(250t+1)
And, A is 250 hectares
.
Then, you have:
250 = 60log(250t+1)
Solving for t:
250 = 60log(250t+1)
250/60 = log(250t+1)
250/60 = log(250t+1)
4.1667 = log(250t+1)
10^4.1667 = 250t+1
14677.993 = 250t+1
14676.993 = 250t
58.71 hours = t
or
2 days 10 hours 42 minutes 29 seconds