Mathematical expression of Moore’s law
https://en.wikipedia.org/wiki/Moore%27s_law
e^(t)=2, what is t?
t = Log_e(2). Plug this t expression back into the first expression:
e^(log_e(2) *t/2) = y. This is Moore’s law function, natural logarithm based.
For a 10-base logarithm function:
10^(t)=2, what is t? Log_10(2) = t. Plug this t as before and arrive to:
10^(log_10(2) * t/2) = y.
ANOTHER EXAMPLE
Number of atoms in the Universe is 10^80. How to rewrite this number to base-2 exponential expression, as in 2^x?
2^x = 10^80
Log_10 (2^x) = Log_10 (10^80)
x * log_10(2) = 80 * log_10(10)
x = 80 * log_10(10) / log_10(2)
log_10(10) = 1
x = 80 / log_10(2) = 2.66e2 = 266,
2^266 = 10^80
Our universe is 2^x = 13.7e9 years old, which is = to log 2^x = log13.7e9, and x=log13.7e9/log2 = 33, hence 13.7e9 = 2^33 years.
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