Logarithmic Functions

A logarithmic function has the form y equals log base n of x. Where the base number n is a numeric constant to be taken to an exponential power to get to the x value. If the base number is not provided then it is assumed to be 10. This function is the inverse function to the exponential function with the same base number. The logarithmic function asks the question what is the exponent needed to take the base number to the value of the independent variable x. The y variable is that exponent. Given a base of 10 and an x value of 1000, then y would be equal to 3, since 10 cubed equals 1000. The natural logarithm function is a special case of the logarithmic function. Here y equals the natural log of x and the special number e is the base number. This equation asks the question, what exponent y is needed for the base number e to get a specified answer x. The natural logarithm function is the inverse function of the exponential function, y equals e to the power of x which has the same base number. The number e is an irrational number defined by a special limit function. The domain of logarithmic functions is from zero to infinity and the range from negative infinity to positive infinity the set of real numbers. This is precisely reversed for the exponential function.

Logarithmic function form:

y = log(x)
y equals log base 10 of x

y = ln(x)
y equals the natural log of x

Logarithmic function base 10:
If y = log(x),
when x = 10,000 then y = 4,
when x = 1,000 then y = 3,
when x = 100 then y = 2,
when x = 10 then y = 1.

Natural logarithmic function base e:
If y = ln(x),
when x = e then y = 1.