Question 225276
{{{N(t) = 20(3)^t}}}
You're given n(t) =1000 and you've been asked to find t:
{{{1000  = 20(3)^t}}}
So solve for t we're going to "peel away" the rest of the right side (i.e. the 20 and the 3). We'll start by dividing both sides by 20:
{{{50 = 3^t}}}
Next, to get rid of the 3, we will need to use logarithms. If 50 and {{{3^t}}} are equal then their logarithms are equal, too. (You should use a base for the logarithms that your calculator can handle. Usually base 10 or base e (aka natural) logarithms are best.):
{{{log((50)) = log((3^t))}}}
Now we can use the property of logarithms, {{{log(a, (b^c)) = c*log(a, (b))}}}, to "move" the t out of the exponent:
{{{log((50)) = t*log((3))}}}
We can now solve for t by dividing both sides by {{{log((3))}}}:
{{{log((50))/log((3)) = t}}}
For our final answer we can use our calculator on the two logarithms on the left side:
{{{1.6989700043360188047862611052755/0.47712125471966243729502790325512 = t}}}
{{{3.5608767950073117714936079297 = t}}}
Of course you can round off these decimals as you prefer.