1. On your graph paper, draw the graphs y = 2 x and y = 3 x These are both types of exponential functions Extension: Sketch these graphs and comment on their transformation from y = 2 x or y = 3 x a). y = 2 x + 5 b). y = 2 x – 3 c). y = 3 2x d). y = 2 -x

2. Solving exponential equations Can you find the value of x in the following? a. 2 x = 8 b. 3 x = 81 c. 5 x = 0.2 d. 10 x = 1,000 e. 49 x = 7 f. 2 x = 10 You could use your graphs to help with these…

3. Logs can help with equations like 2 x = 10 Let’s check our answers to these equations using logs: a. 2 x = 8 b. 3 x = 81 c. 5 x = 0.2 d. 10 x = 1,000 e. 49 x = 7 f. 2 x = 10

6. On your calculators, check log3 + log4 = log12 Can you explain why this works?

7. Using the log laws:

9. Recap from last Thursday: *logs are great for finding powers, eg. 2 x = 10, x = log 2 10 *b x = a can be rearranged to x = log b a *there are 3 log laws : log a m + log a n = log a mn log a m - log a n = log a m/n log a m k = klog a m *exponential graphs have a special shape:

10. Using logs and log laws to solve equations 3 sig figs a.4 x = 28 b.5 2x + 1 = 8 c.2 4 - 6x x 2 9x + 1 = 128 d.5 2x – 3(5 x ) + 2 = 0 (Hint: try solving m 2 – 3m + 2 = 0 first) e. log 4 (2x + 1) + log 4 3 = 2 f. 2log 4 x – log 4 (x + 24) = 1 g. Find the coordinate of y = 2 x – 7 intersects the x- axis.