Presentation on theme: "Logs and Exp as inverses"— Presentation transcript:
1 Exponential and logarithmic operations undo each other since they are inverse operations.
2 Logs and Exp as inverses WHY!Rewrite it as a logarithm
3 Example 4: Recognizing Inverses Simplify each expression.a. log3311b. log381c. 5log510log3311log33 3 3 35log51011log334104
4 Check It Out! Example 4a. Simplify log100.9b. Simplify 2log2(8x)log 100.92log2(8x)0.98x
5 Most calculators calculate logarithms only in base 10 or base e (see Lesson 7-6). You can change a logarithm in one base to a logarithm in another base with the following formula.
6 Example 5: Changing the Base of a Logarithm Evaluate log328.Method 1 Change to base 10log328 =log8log320.9031.51≈Use a calculator.Divide.≈ 0.6
7 Method 2 Change to base 2, because both 32 and 8 are powers of 2. Example 5 ContinuedEvaluate log328.Method 2 Change to base 2, because both 32 and 8 are powers of 2.log328 =log28log232=35Use a calculator.= 0.6
8 Check It Out! Example 5a Evaluate log927. Method 1 Change to base 10. 1.4310.954≈Use a calculator.≈ 1.5Divide.
9 Check It Out! Example 5a Continued Evaluate log927.Method 2 Change to base 3, because both 27 and 9 are powers of 3.log927 =log327log39=32Use a calculator.= 1.5
10 Check It Out! Example 5b Evaluate log816. Method 1 Change to base 10. 1.2040.903≈Use a calculator.Divide.≈ 1.3
11 Check It Out! Example 5b Continued Evaluate log816.Method 2 Change to base 4, because both 16 and 8 are powers of 2.log816 =log416log48=21.5Use a calculator.= 1.3
13 Logarithmic scales are useful for measuring quantities that have a very wide range of values, such as the intensity (loudness) of a sound or the energy released by an earthquake.The Richter scale is logarithmic, so an increase of 1 corresponds to a release of 10 times as much energy.Helpful Hint
14 Use a calculator to find each logarithm to the nearest thousandth. Lesson Quiz: Part IIUse a calculator to find each logarithm to the nearest thousandth.7. log3202.7278. log 1012–3.322