7.4 Exponential equations
Unit 7 · Exponential and logarithmic functions
Ideas in this lesson
Use a common base
Rewrite both sides with the same one-to-one exponential base, then equate exponents.
Solve with logarithms
Isolate the exponential, take logarithms and divide by the coefficient of the variable.
Quadratic exponential substitutions
Replace a repeated positive exponential by a new variable, factor, then reject nonpositive values of the new variable.
Exponential inequalities
An increasing exponential preserves an inequality; a decreasing exponential reverses it when comparing exponents.
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