LOGARITHM
The logarithm of a numver is the exponent to which another fixed value ,the base, must be raised to produce that number.For example, the logarithm of 1000 to base 10 is 3 , because 1000 to the power 3:1000 = 10.10.10 = 10^3. More generally if x= b^y, then y is the logarithm of x to base b, and is written y = logb(x) so log10(1000) = 3.The present day notion of logarithms comes from Leonhard Euler ,
who connected to the exponential function in the 18th century.
who connected to the exponential function in the 18th century.
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The idea of logarithms is to reverse the operation of exponentiation, thar is raising a number
to a power.For example, the third power (or cube) of 2 is 8 ,because 8 is the product of
three factors of 2 :
to a power.For example, the third power (or cube) of 2 is 8 ,because 8 is the product of
three factors of 2 :
It follows that the logarithm of 8 with respect to base 2 is 3, so log2 8 = 3.
The logarithm of a positive real number x with respect to base b, a positive real number not equal to 1[nb 1],
is the exponent by which b must be raised to yield x. In other words, the logarithm of x to base b is
the solution y to the equation[2]
is the exponent by which b must be raised to yield x. In other words, the logarithm of x to base b is
the solution y to the equation[2]
The logarithm is denoted "logb(x)" (pronounced as "the logarithm of x to base b" or "the base-b logarithm of x").
You can watch the video to understand more efficient.
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