![]() Plots on paper with one log scale can show up exponential laws, and on log-log paper power laws, as straight lines (see semilog graph, log-log graph). Logarithmic graph paper, before the advent of computer graphics, was a basic scientific tool. The geometric mean of two numbers is midway between the numbers. Horizontal Shift If h > 0, the graph would be shifted left. If k < 0, the graph would be shifted downwards. Vertical shift If k > 0, the graph would be shifted upwards. The domain consists of positive real numbers, (0,) and the range. The x-axis has a linear scale, which means the ticks are evenly spaced. The logarithmic function, y log b ( x), can be shifted k units vertically and h units horizontally with the equation y log b ( x h) k. Graphing Logarithmic Functions We can use the translations to graph logarithmic functions. In a semi-log graph the y-axis is logarithmic, which means the seperation between the ticks on the graph is proportional to the logarithm of numbers. Semi-log Graph The first is called a semi-log graph. On a logarithmic scale an equal difference in order of magnitude is represented by an equal distance. There are two types of log graphs that can be used when plotting data. A slide rule has logarithmic scales, and nomograms often employ logarithmic scales.
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