8-3 Logarithm Functions as Inverses Hubarth Algebra II

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 Ex. 1 Real-World Connection Richter Scale E

Ex. 2 Writing in Logarithm 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. Write: 32 = 2 5 in logarithmic form.

Ex. 3 Evaluating Logarithms Evaluate log 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.

(1, 10) (0, 1) (1, 0) (10, 1)

Ex. 5 Graphing a Logarithmic Function 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.

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 –3 –2 –1 0 1 x y = log 5 x

Practice