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7.3 Presentation Transcript

  • 1. 7.3 LOGARITHMICFUNCTIONS ASINVERSESPart 1: Introduction to Logarithms
  • 2. Logarithms The inverse of the exponential function is the logarithmic function.  By definition, y = bx is equivalent to logby = x.  Logarithms exist only for positive real numbers.
  • 3. Logarithms The definition of a logarithm can be used to write exponential functions in logarithmic form: y = bx is equivalent to logby = x
  • 4. Example:Write each equation in logarithmic form100 = 102y = bx is equivalent to logby = x
  • 5. Example:Write each equation in logarithmic form81 = 34y = bx is equivalent to logby = x
  • 6. Logarithms To write a logarithmic function in exponential form, use the definition: If y = bx is equivalent to logby = x, then logby = x is equivalent to y = bx
  • 7. Example Write each equation in exponential form. log2128 = 7 logby = x is equivalent to y = bx
  • 8. Example Write each equation in exponential form. log716,807 = 5 logby = x is equivalent to y = bx
  • 9. Logarithms The exponential form of a logarithm can be used to evaluate a logarithm. 1. Write a logarithmic equation (set the log = x) 2. Use the definition to write the logarithm in exponential form 3. Write each side of the equation using the same base 4. Set the exponents equal to each other 5. Solve
  • 10. Example: Evaluate each logarithm log5125
  • 11. Example: Evaluate each logarithm log832
  • 12. Example: Evaluate each logarithm
  • 13. Common Logarithm The common logarithm is a logarithm with base 10 log10  The common logarithm can be written without a base, because it is understood to be 10 log10x = log x  The“log” key on your calculator is the common logarithm
  • 14. Homework P456 #12 – 35