MTH-100 Lecture Notes - Liquid Oxygen
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Proofs appear at end of notes xy log ( b log x y b. Properties of logarithms b b (2) log (1) log 1 0. Example 1. log (3x2) log 3+ log x2 log 3 + 2 log x. Use the properties of logs to write each expression as a single log. Try: log (x 4) + log (x + 2) Example 4. log (x) + log (x + 3) log [x(x + 3)] Example 5. log(x 2) log(x + 5) log x. Example 7. log(2) log( ) x log( x. Use the change of base formula to calculate. Example 8. log5 500 log5 500 = log 500 log 5. Recall the relationship that y logb x means yb x= Proof of properties (1) logb 1 = 0. Suppose y = logb 1 y = log 1b so yb = . For any base b0 = 1 so y = 0.
