Exponential Equations (Cambridge International AS Mathematics)

Exponential equations

What are exponential equations?

• An equation where the unknown is a power
• In simple cases the solutions can be “spotted”

How do I solve exponential equations?

• Laws of Indices are often needed to rewrite equations
• Laws of Logarithms are used to solve exponential equations
• ln (log_e) is often used
• Answers are often written in terms of ln

How do I solve hidden quadratic exponential equations?

• Look out for “hidden” squared terms, these are hidden quadratics which will need to be solved

  • 4^x= (2²)^x= 2^2x= (2^x)²
  • e^2x= (e²)^x= (e^x)²

Worked Example