Pre-Calculus 12 Notes

By: Gen L.

In partnership with Hyperion University, 2024

Lesson 1: Solving Exponential Equations

On Exponents

You should be familiar with powers of integers:





Exponent Rules

  • Identity
  • Product
  • Quotient
  • Power
  • Distributive Product
  • Distributive Quotient
  • Inverse
  • Reciprocal
  • Fractional

On Exponent Rules

  • They all deal with multiplication and division.
  • Must have SAME base to combine
  • Fractional Exponents are radicals in disguise.
  • Quite often, you'll convert radicals to rational exponents instead

Solving Exponential Equations

Strategy: if

When Solving:

  • Get the same base
  • set exponents equal to each other

Solving Exponentials

Solving Exponentials, cont.

Solving, cont.

    • Identity Law:
    • Isolate the exponential

Solving, cont.

    • Isolate the exponential

Simplifying

Solving is very different from simplifying. The big difference is that solving has an = sign. Make sure to check whether to simplify or solve.

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