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Logarithmic Functions

Logarithmic Functions. Section 6.3. Use the table below. Use the table to find x in each equation. A. 10 x = 1000 B. C. On your graphing calculator: 1. Enter the equation 2. See the table of values for this equation by pressing 2 nd table. 3. What is 10 7 ?

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Logarithmic Functions

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  1. Logarithmic Functions Section 6.3

  2. Use the table below. • Use the table to find x in each equation. • A. 10x = 1000 • B. • C.

  3. On your graphing calculator: • 1. Enter the equation • 2. See the table of values for this equation by pressing 2nd table. • 3. What is 107? • 4. Now change the table setup so the x values change by 0.01 by pressing 2nd table set • 5. Arrow down to tbl and change to 0.01 • 6. Go back to the table and approximate x for

  4. To solve an equation such as 10x = 85 or 10x = 2.3 a logarithm is needed. • With logarithms you can write an exponential equation in an equivalent logarithmic form.

  5. Exponential form Logarithmic form • 103 = 1000 3 = log10 1000 base exponent

  6. Equivalent exponential and logarithmic forms • For any positive base b, where bx = y if and only if x = logb y • Examples: Write each equation in exponential form. • 1. log2 8 = 3 8 = 23 • 2.

  7. 3. log39 = 2 32 = 9 • 4. log8512 = 3 83 = 512 • 5. log5625 = 4 54 = 625 • Write each equation in logarithmic form. • 1. 153 = 3375 log153375 = 3

  8. 2. log42 = ½ • 3. 53 = 125 log5125 = 3 • 4. log273= 1/3 • 5. 113 = 1331 log111331 = 3

  9. Evaluate logarithmic expressions using your calculator • You can evaluate logarithms with a base of 10 by using the log key on a calculator. • Find the approximate value of each logarithmic function. Round to the nearest tenth. • 1. log10 870 = 2.9 • 2. log1098,560 = 5.0 • 3. log10.0000056 = -5.3

  10. Solve 10x = 85 for x. Round to the nearest hundredth. • Write the equation in logarithmic form and use the log key. • x = log10 85 • Solve 10x = 14.5 for x. Round to the nearest hundredth. • x = log10 14.5

  11. Day 2 • Evaluate without a calculator. • Ex 1 • Ex. 2 • Ex. 3 • Ex. 4

  12. Day 2 • Case 2: Solving using rational exponents • When: Use when the variable is the base of an exponential expression. • How: Raise both side of the equation to the reciprocal of the power of the exponent.

  13. Examples. • Ex. 1 Ex 2.

  14. Ex. 3 Ex. 4

  15. Case 3: One-to-One Property of Exponents: If bx = by, then x = y • When to use: bases are the same number or can be changed to the same number • How: set exponents equal. • Note: will be on non-calculator portion quiz/test

  16. Ex. 1 Ex. 3 • Ex. 2

  17. Solve for v. • Write in exponential form and solve. • Ex. v = log125 5 • 125v = 5 • (53)v = 5 • 53v = 51 • 3v = 1 • v = 1/3

  18. Ex. 2v = 1 • v = 0 • (remember: any base raised to the zero power = 1)

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