Let b and y be positive numbers, b can't be 1. log base b y = x if and only if b^x=y
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The base b logarithm of x is a value y such that by = x
The logarithm of 1 to the base 1 is indeterminate. The logarithm of a number x to the base a is a number y, such that ay = x. The most common base a is 10, or the natural base a is e (2.718281828...). It is invalid to think of logarithms base 1, because 1 to the power of anything is still 1.
Logarithm is the solution, "x", to the equation: ax = b. In this case, assuming the logarithm is base 10, 10x = 1; the same for any other base.
The main use for a logarithm is to find an exponent. If N = a^x Then if we are told to find that exponent of the base (b) that will equal that value of N then the notation is: log N ....b And the result is x = log N ..........b Such that b^x = N N is often just called the "Number", but it is the actuall value of the indicated power. b is the base (of the indicated power), and x is the exponent (of the indicated power). We see that the main use of a logarithm function is to find an exponent. The main use for the antilog function is to find the value of N given the base (b) and the exponent (x)
The logarithm of 1.5 is approximately 0.1760912591... Your logarithm is base 10, and the natural logarithm of 1.5 (base e), is approximately 0.4054651081... Example base: 8 Approximately: 0.1949875002...