For example, when I try to solve an equation like 1.096 = a^1000, what should I do?

I'm trying to find a formula for this set of data and that's how I got the above equation: d=???
Elevation (ft) Sea level labeled h
1000 2000 3000 4000
Takeoff roll (ft) labeled d
605 663 727 797 873

4 answers

if you know about exponents, you should know about logs, which are the inverse function.

a^1000 = 1.096
1000 log(a) = log(1.096)
a = log(1.096)/1000 = 0.0000917
How did you get the 0.0000917?
I plugged log(1.096) divided by 1000 and got 3.98 times 10 to the -5.
For the data I gave above, we need to find a formula for the exponential function.

I got b to be 605. That part is right at least, right? Because of how 605 = b times a^0 which means b equals 605. (0 because the 605 matches up with sea level in the data--I posted it weirdly)

So then plugging b into the second set of data given, 663 = 605 times a^1000.
So 1.096 = a^1000
and then inserting what you taught me,
1000 log a = log 1.096
and so if a = 0.0000917, the formula of the function would be y=605 times 0.0000917^x?
We may have taken different logs. Base 10 vs base e.

Looks good to me. Does this fit any of the other data points very well?