Graph of Logarithms of Fractions

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 Source: How does the graph of logarithms of fractions look like. - Search (bing.com)

The graph of a logarithmic function, including those involving fractions, has a characteristic shape. The function is defined as (y = \log_b(x)), where (b > 0) and (x > 0).

The graph of the logarithmic function is a curve that lies entirely in the first and fourth quadrants (if we consider the standard Cartesian coordinate system). It has the following properties:

  1. The graph is always increasing if the base (b > 1).
  2. The graph passes through the point (1, 0), because (\log_b(1) = 0) for any base (b).
  3. The graph approaches the y-axis (the line (x = 0)) but never touches or crosses it. This vertical line is a vertical asymptote of the function.
  4. The graph is continuous and smooth, with no sharp turns or corners.

When (x) is a fraction between 0 and 1, the value of (y = \log_b(x)) is negative. This is because the logarithm of a fraction between 0 and 1 is negative. For example, (\log_{10}(0.1) = -1), (\log_{10}(0.01) = -2), and so on.

So, when you graph logarithms of fractions, the graph will dip below the x-axis. The smaller the fraction, the further down the graph will go12.

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