IV. Logarithmic Functions a. In(x) = logex = natural logarithm b. logx = log10x - common logarithm c. log. = y; ax = x d. Domain: (0, ) e. Range: (-co, 00) f. Graphs have vertical asymptotes which are affected by horizontal shifts g. Graphs of logarithmic functions (for a > 0) are concave down, continuous everywhere, and differentiable everywhere on its domain h. Example: Find domain i. y = logs(x+3) ii. vertical asymptote: x = -3 iii. Domain: (-3, ) iv. Range: (-co, 00) V. vi. vii. 1. There is no graph on the left-hand side of x = -3 viii. REMARK: Near a vertical asymptote, the graph always goes to either co or - 0 i. Example: Find the domain i. y = log(lnx) ii. Inx > 0 iii. x > e iv. x > 1; (1,). v. graphically, Inx > 0; where is the graph of Inx above the x-axis