The Logarithmic Function

Pure Mathematics — Second Secondary

The graph of the logarithmic function

The graph of f(x) = loga x is the reflection of the graph of the exponential function f(x) = ax in the line y = x.
It has these features:

It always passes through the point (1, 0), because log_a 1 = 0.
The y-axis (x = 0) is a vertical asymptote, and the curve approaches it without touching it.
If a > 1 the function is increasing, and if 0 < a < 1 the function is decreasing.

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