Question

inverse exponential processing, say N = 10000, N=10^x.  How can we  solve for value of X?

Answer 1

Question: inverse exponential processing, say N = 10000, N=10^x. How can we solve for value of X?

For this simple case, write N as a power of 10.

 viz. N = 10,000 = 10^4.

i.e. N = 10^4 = 10^X

Hence X = 4.

For a non-simple case, where N is not an integer power of 10, then use logs.

We would have,

N  = 10^X

ln(N) = ln(10^X) = X*ln(10)

Hence, X = ln(N)/ln(10)

e.g. N = 15,321, then

ln(15321) = X*ln(10)

X = ln(15321)/ln(10) = 9.6369797/2.302585

X = 4.185287

If you put that value in a calculator, and then raise 10 to that power, you will get 15,321 in your results display.