1. Compare the amount of energy released in an earthquake that registers 6 on the Richter scale with one that registers 3. = 30 6–3 Division Property of Exponents = 30 3 Simplify. = 27,000Use a calculator. The first earthquake released about 27,000 times as much energy as the second. Write a ratio. E 30 6 E 30 3 = Simplify. 30 6 30 3 ALGEBRA 2 LESSON 8-3 Logarithmic Functions as Inverses 8-3

2. Write: 32 = 2 5 in logarithmic form. If y = b x, then log b y = x.Write the definition. If 32 = 2 5, then log 2 32 = 5.Substitute. The logarithmic form of 32 = 2 5 is log 2 32 = 5. ALGEBRA 2 LESSON 8-3 Logarithmic Functions as Inverses 8-3

3. Evaluate log 3 81. Let log 3 81 = x. Log 3 81 = x Write in logarithmic form. 81 = 3 x Convert to exponential form. 3 4 = 3 x Write each side using base 3. 4 = x Set the exponents equal to each other. So log 3 81 = 4. ALGEBRA 2 LESSON 8-3 Logarithmic Functions as Inverses 8-3

4. The pH of an apple is about 3.3 and that of a banana is about 5.2. Recall that the pH of a substance equals –log[H + ], where [H + ] is the concentration of hydrogen ions in each fruit. Which is more acidic? The [H + ] of the apple is about 5.0  10 – 4. The [H + ] of the banana is about 6.3  10 – 6. The apple has a higher concentration of hydrogen ions, so it is more acidic. ALGEBRA 2 LESSON 8-3 Logarithmic Functions as Inverses 8-3 Apple pH = –log[H + ] 3.3 = –log[H + ] log[H + ] = –3.3 [H + ] = 10 –3.3 5.0  10 – 4 [H + ] = 10 –5.2 pH = –log[H + ] 5.2 = –log[H + ] log[H + ] = –5.2 Banana 6.3  10 – 6

5. Graph y = log 4 x. By definition of logarithm, y = log 4 x is the inverse of y = 4 x. Step 1: Graph y = 4 x. Step 2: Draw y = x. Step 3: Choose a few points on 4 x. Reverse the coordinates and plot the points of y = log 4 x. ALGEBRA 2 LESSON 8-3 Logarithmic Functions as Inverses 8-3

6. Step 2: Graph the function by shifting the points from the table to the right 1 unit and up 2 units. Graph y = log 5 (x – 1) + 2. Step 1: Make a table of values for the parent function. 1 125 1 25 1515 1 5 –3 –2 –1 0 1 x y = log 5 x ALGEBRA 2 LESSON 8-3 Logarithmic Functions as Inverses 8-3