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Section 5.3 Properties of Logarithms

Section 5.3 Properties of Logarithms. Advanced Algebra. Properties of Logarithms. log b 1 = 0 Anything raised to the 0 power is 1. log b b = 1 Anything raised to the 1st power is that anything log b b x = x Think about as exponent: b x = b x Rewrite as a log: log b x = log b x.

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Section 5.3 Properties of Logarithms

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  1. Section 5.3 Properties of Logarithms Advanced Algebra

  2. Properties of Logarithms • logb1 = 0 • Anything raised to the 0 power is 1. • logbb = 1 • Anything raised to the 1st power is that anything • logbbx = x • Think about as exponent: bx = bx • Rewrite as a log: logbx = logbx

  3. log 1 = 0 log 10 = 1 log 10x = x 10log x = x x > 0 ln 1 = 0 ln e = 1 ln ex = x eln x = x if x > 0 Common and Natural Log Properties

  4. Simplifying

  5. Simplify Using Properties

  6. More Simplifying

  7. More Simplifying

  8. More Simplifying

  9. 3 More Properties • Product Rule • logbMN = logbM + logbN • Quotient Rule • Power Rule

  10. Write as a sum or difference of logs

  11. Expand as a sum and difference of logs

  12. Expand the log into a sum or difference of logs

  13. Write the difference as a single log

  14. Write the sum as a single log To use the product or quotient rules of logs, remember, the bases must be the same.

  15. Combine into a single log

  16. Condense to a single logarithm

  17. Evaluate log45 Change of Base Formula

  18. Evaluate

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