The function y = log_b(x) is the inverse of y = b^x. Key features of y = log_b(x) (for b > 1): - Domain: x > 0 (only positive inputs) - Range: all real nu…
The function y = log_b(x) is the inverse of y = b^x. Key features of y = log_b(x) (for b > 1): - Domain: x > 0 (only positive inputs) - Range: all real numbers - Passes through (1, 0) always (because log_b(1) = 0) - Passes through (b, 1) (because log_b(b) = 1) - Vertical asymptote at x = 0 (y-axis) - Increasing (slowly) as x grows The graph is a reflection of y = b^x across the line y = x.
Example: What is the vertical asymptote of y = log_3(x - 2)?
Remember: log graphs always have a vertical asymptote where the argument equals 0, and they always pass through the point where the argument equals 1 (giving y = 0). For y = log_b(x - h) + k, the asymptote is x = h and the point (h+1, k) is on the graph.
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