pH is a logarithmic scale; because of the way calculus and maths works, graphing such a scale against a log results in a straight line.
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The graph of y = log(x) is defined only for x>0. The graph is a monotonic increasing function over its domain. It starts from an asymptotic "minus infinity" when x approaches 0. It passes through the value y = 0 when x = 1. The graph is illustrated at the link below.
An exponential function can be is of the form f(x) = a*(b^x). Some examples are f1(x) = 3*(10^x), or f2(x) = e^(-2*x). Note that the latter still fits the format, with b = e^(-2). The inverse is the logarithmic function. So for y = f1(x) = 3*(10^x), reverse the x & y, and solve for y:x = 3*(10^y)log(x) = log(3*(10^y)) = log(3) + log(10^y) = log(3) + y*log(10) = y*1 + log(3)y = log(x) - log(3) = log(x/3)The second function: y = e^(-2*x), the inverse is: x = e^(-2*y).ln(x) = ln(e^(-2*y)) = -2*y*ln(e) = -2*y*1y = -ln(x)/2 = ln(x^(-1/2))See related link for an example graph.
For a quotient x/y , then its log is logx - log y . NOT log(x/y)
A log-log scale is a set of axes where each axis is logarithmic in scale.
to log in friendster.com