1. Logarithmic Equations Unknown Exponents Unknown Number Solving Logarithmic Equations Natural Logarithms

2. Logarithmic Equations Key Point: Logarithmic equations can be solved either in logarithmic form or in exponential form. log N = x 10 X = N

3. Unknown Exponents Key Point: Logarithmic equations can be solved directly when the exponent is unknown. x = log 250 = 2.40

4. Unknown Number Key Point: Change from logarithmic to exponential form when the number is unknown. log a = 7.83 a = 10 7.83 = 6.76 X 10 7

5. Solving Logarithmic Equations Key Point: We solve logarithmic equations using rules developed in Chapter 7.

6. Natural Logarithms Key Point: Equations involving natural logarithms are solved just like equations involving common logarithms. e y = 83. Solve for y. y ln e =ln 83 y(1) = In 83 y = 4.42