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Graphs of Logarithmic Functions

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State

The graph of log_b(x) has domain (0, ∞), passes through (1, 0), and falls along the vertical asymptote x = 0 — the exponential's picture reflected across y = x.

Show

log₂ runs through (1, 0), (2, 1), (8, 3); near zero it plunges — log₂(1/1024) = −10, deep and deeper.

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