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Algebra readiness

Work with indices and exponential equations · Diagrams

Exponential and logarithm graphs for both base ranges

Compare exponentials and logarithms

Domain: all real inputs. Range: y > 0. The curve increases; y = 0 is a horizontal asymptote, never an attained value.

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Choose an exponential or logarithm method

  1. Check the base and domain.
  2. Rewrite using a common base or logarithms.
  3. Check answers in the original equation.
Four source graph cases. With a>1 the exponential increases through (0,1) and logarithm increases through (1,0); with 0<a<1 each decreases through the same respective intercept. Exponentials stay above the x-axis; logarithms have domain x>0 and vertical asymptote x=0. Curves are schematic.
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