What are exponential equations?

• An exponential equation is an equation where the unknown is a power
  • In simple cases the solution can be spotted without the use of a calculator
  • For example,

• In more complicated cases the laws of logarithms should be used to solve exponential equations

• The?change of base?law can be used to solve some exponential equations without a calculator
  • For example,

How do we use logarithms to solve exponential equations?

• An exponential equation can be solved by taking logarithms of both sides
• The?laws of indices?may be needed to rewrite the equation first
• The?laws of logarithms?can then be used to solve the equation
  • ln (log_e)?is often used
  • The answer is often written in terms of ln
• A question my ask you to give your answer in a particular form
• Follow these steps to solve exponential equations
  • STEP 1: Take logarithms of both sides
  • STEP 2: Use the laws of logarithms to remove the powers
  • STEP 3: Rearrange to isolate?x
  • STEP 4: Use logarithms to solve for?x

What about hidden quadratics?

• Look for hidden squared terms that could be changed to form a quadratic
  • In particular look out for terms such as
    • 4^x?= (2²)^x?= 2^2x?= (2^x)²
    • e^?2x?= (e²)^x?= (e^x)²