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# Alg2 lesson 10-4 and 10-5

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### Transcript

• 1. A common logarithm has a base of 10.<br /> log 5 means log10 5<br />The log key on your calculator will find common logs.<br />
• 2. Solve<br />Example 4-3a<br />
• 3. Solve<br />log 3x = log 17<br />x log 3 = log 17<br />x = <br />log 17log 3<br />1.23040.4771<br />=<br />= 2.5789<br />Example 4-3c<br />
• 4. Solve:<br />
• 5. Solve: 5x + 3 = 2x+4<br />log 5x + 3 = log 2x+4<br />(x + 3) log 5 = (x + 4) log 2<br />x log 5 + 3 log 5 = x log 2 + 4 log 2<br />x log 5 – x log 2 = 4 log 2 – 3 log 5<br />x(log 5 – log 2) = 4 log 2 – 3 log 5<br />x = 4 log 2 – 3 log 5 log 5 – log 2 <br />= 4(0.3010) – 3(0.6990) 0.6990 – 0.3010<br />= -2.244<br />
• 6. Change of base formula<br />
• 7. Find <br />Example 4-5a<br />
• 8. Find<br />Example 4-5b<br />
• 9. Quantities that grow or decay continuously can be described by a natural exponential function.<br /> f(x) = ex<br />e is a constant <br />e is approximately 2.71828<br />
• 10. Use a calculator to evaluate each expression to four decimal places.<br />a.<br />b.<br />Answer:1.3499<br />Answer:0.1353<br />Example 5-1c<br />
• 11. The inverse of the natural exponential function is the natural log function.<br />y = ex loge x = y<br />loge is usually written as ln<br />
• 12. Use a calculator to evaluate each expression to four decimal places.<br />a. In 2<br />b. In <br />Answer:0.6931<br />Answer:–0.6931<br />Example 5-2f<br />
• 13. Write as a natural logarithmic equation. <br />x = loge23<br />x = ln23<br />Example 5-3a<br />
• 14. Write as an exponentialequation.<br />loge x = 2.25<br />Example 5-3c<br />