1. EXAMPLE 7 Graph logarithmic functions Graph the function. SOLUTION a.y = 3 log x Plot several convenient points, such as (1, 0), (3, 1), and (9, 2). The y -axis is a vertical asymptote. From left to right, draw a curve that starts just to the right of the y -axis and moves up through the plotted points, as shown below.

2. EXAMPLE 7 Graph logarithmic functions Graph the function. SOLUTION b.y = 1/2 log x Plot several convenient points, such as (1, 0), (2, –1), (4, –2), and (8, –3). The y -axis is a vertical asymptote. From left to right, draw a curve that starts just to the right of the y -axis and moves down through the plotted points, as shown below.

3. EXAMPLE 8 Translate a logarithmic graph SOLUTION STEP 1 Graph. State the domain and range. y = 2 log (x + 3) + 1 STEP 2 Sketch the graph of the parent function y = x, which passes through (1, 0), (2, 1), and (4, 2). 2 log Translate the parent graph left 3 units and up 1 unit. The translated graph passes through (–2, 1), (–1, 2), and (1, 3). The graph’s asymptote is x = –3. The domain is x > –3, and the range is all real numbers.

4. GUIDED PRACTICE for Examples 7 and 8 Graph the function. State the domain and range. SOLUTION 16.y = 5 log x If x = 1 y = 0, x = 5 y = 1, x = 10y = 2 Plot several convenient points, such as (1, 0), (5, 1), and (10, 2). The y -axis is a vertical asymptote.

5. GUIDED PRACTICE for Examples 7 and 8 From left to right, draw a curve that starts just to the right of the y -axis and moves up through the plotted points. The domain is x > 0, and the range is all real numbers.

6. GUIDED PRACTICE for Examples 7 and 8 Graph the function. State the domain and range. SOLUTION 17.y = 1/3 log (x – 3) domain: x > 3, range: all real numbers

7. GUIDED PRACTICE for Examples 7 and 8 Graph the function. State the domain and range. SOLUTION 18.y = 4 log (x + 1) – 2 domain: x > 21, range: all real numbers