How are the logs coming about? thanks
1 Answer
A few thoughts...
Explanation:
I am not exactly sure what you are asking, but here's something of what logarithms are about...
Let
Consider the function:
#f(x) = b^x#
This is a continuous, one to one, strictly monotonically increasing function from
graph{2^x [-9.58, 10.42, -2.4, 7.6]}
It has the interesting property that:
#f(x+y) = b^(x+y) = b^x b^y = f(x)f(y)#
for any
The inverse of
graph{2^y-x = 0 [-4.08, 15.92, -4.12, 5.88]}
which is a continuous, one to one, strictly monotonically increasing function from
Given any
#x = f^(-1)(u)#
#y = f^(-1)(v)#
Then we find:
#f^(-1)(uv) = f^(-1)(f(x)f(y)) = f^(-1)(f(x+y)) = x+y = f^(-1)(u)+f^(-1)(v)#
This inverse function
and this property we have found is:
#log_b(uv) = log_b(u)+log_b(v)#
a fundamentally useful property of logarithms.
This property of logarithms was discovered by John Napier in the 17th century and used in the form of slide rules and tables to help perform calculations.