Math
posted by Lisa .
You invest $500 @ 6.5% compound annually given by the equation A=500(1.065)ⁿ where n=number of years and A=amount earned.
How long would it take to earn $1000?

1000 = A; n = years.
1000 = 500(1.065)^{n}
1000/500 = 2 = (1.065)^{n}
log 2 = n*log 1.065
0.30103 = n*0.02735
n = 0.30103/0.02735
n=11 years. 
wow thanks so much!
what does the log button mean exactly?
what does it do? 
The log button provides the logarithm (base 10) of any number punched into the calculator. (There is also an ln button on most calculators that provides the logarithm (base e) of any number punched into the calculator. There is probably a way of solving that equation without using logs but I don't know how to do it. I know that log x^{y} is the same as y*log x and I let the calculator and algebra do the rest. A quick lesson in logs.
The definition of logarithm (I'll use base 10) is the power to which 10 must be raised to give that numbers. Sounds confusing but all it means is that the
log 10 = 1 BECAUSE 10^{1} = 10.
log 100=2 BECAUSE 10^{2} = 100.
log 1000=3 because 10^{3} = 1000 etc. Logs of numbers between 1 and 10 must be looked up on a calculator or in a set of tables since they are not whole numbers like 1 and 2 and 3. Hope this helps. 
I have this exact same question, but in my assignment I'm told I have to make a table of values, graph whatever it is, find the x&y intercepts, find the domain and range, determine whether it's increasing or decreasing, the equation of the asymptote, and what is the implication of the asymptote related to caffeine in the body.

* disregard the caffeine comment. sorry about that.