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Example 1 Find Common Logarithms A. Use a calculator to evaluate log 6 to the nearest ten-thousandth. Answer: about Keystrokes: ENTER LOG

Example 1 Find Common Logarithms B. Use a calculator to evaluate log 0.35 to the nearest ten-thousandth. Answer: about – Keystrokes: ENTER LOG.35 –

Example 1 A B C D.100, A. Which value is approximately equivalent to log 5?

Example 1 A.– B C D B. Which value is approximately equivalent to log 0.62?

Example 2 Solve Logarithmic Equations Original equation JET ENGINES The loudness L, in decibels, of a sound is where I is the intensity of the sound and m is the minimum intensity of sound detectable by the human ear. The sound of a jet engine can reach a loudness of 125 decibels. How many times the minimum intensity of audible sound is this, if m is defined to be 1?

Example 2 Solve Logarithmic Equations Exponential form Answer: The sound of a jet engine is approximately 3 × or 3 trillion times the minimum intensity of sound detectable by the human ear. Use a calculator. I ≈ × Replace L with 125 and m with 1. Divide each side by 10 and simplify.

Example 3 Solve Exponential Equations Using Logarithms Solve 5 x = 62. Round to the nearest ten-thousandth. 5 x = 62Original equation log 5 x = log 62Property of Equality for Logarithms x log 5= log 62Power Property of Logarithms Answer: about x≈ Use a calculator. Divide each side by log 5.

Example 3 Solve Exponential Equations Using Logarithms CheckYou can check this answer by using a calculator or by using estimation. Since 5 2 = 25 and 5 3 = 125, the value of x is between 2 and 3. Thus, is a reasonable solution.

Example 3 A.x = B.x = C.x = D.x = What is the solution to the equation 3 x = 17?

Example 4 Solve Exponential Inequalities Using Logarithms Solve 3 7x > 2 5x – 3. Round to the nearest ten-thousandth. 3 7x > 2 5x – 3 Original inequality log 3 7x > log 2 5x – 3 Property of Inequality for Logarithmic Functions 7x log 3> (5x – 3) log 2Power Property of Logarithms

Example 4 Solve Exponential Inequalities Using Logarithms 7x log 3> 5x log 2 – 3 log 2 Distributive Property 7x log 3 – 5x log 2> – 3 log 2Subtract 5x log 2 from each side. x(7 log 3 – 5 log 2)> –3 log 2Distributive Property

x > – Simplify. Example 4 Solve Exponential Inequalities Using Logarithms Use a calculator. Divide each side by 7 log 3 – 5 log 2.

Example 4 Solve Exponential Inequalities Using Logarithms Check: Test x = x > 2 5x – 3 Original inequality Answer: The solution set is {x | x > –0.4922}. ? 3 7(0) > 2 5(0) – 3 Replace x with 0. ? 3 0 > 2 –3 Simplify. Negative Exponent Property

Example 4 A.{x | x > –1.8233} B.{x | x < } C.{x | x > –0.9538} D.{x | x < –1.8233} What is the solution to 5 3x < 10 x – 2 ?

Example: Change of Base Formula

Example 5 Change of Base Formula Express log in terms of common logarithms. Then round to the nearest ten-thousandth. Answer: The value of log is approximately Use a calculator. Change of Base Formula

Example 5 What is log 5 16 expressed in terms of common logarithms? A. B. C. D.

Homework p. 495 # 1 – 12, (x3)

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