How do I solve x = 3y ? John Napier was a Scottish theologian and mathematician who lived between 1550 and 1617. He spent his entire life seeking knowledge, and working to devise better ways of doing everything from growing crops to performing mathematical calculations. He invented a new procedure for making calculations with exponents easier by using what he called logarithms. A logarithm can be written as a function y = logbx. The notation y = logbx is another way of writing x = by. So x = by and y = logbx represent the same functions. y =log3x is simply another way of writing x = 3y. The notation is read “y is equal to the logarithm, base 3, of x.”

Logarithmic Function (Common) Calculator: y1= log(x) Domain: x > 0 or x  (0,∞) Range: y   or y  (-∞,∞) Zeros: (1,0) or x = 1 X-Intercept: (1,0) Y-Intercept: none

Logarithmic Function (Common) Symmetry: None Max: None Min: None Increasing: x  (0,∞) Decreasing: Never Vertical Asymptotes: x = 0 Horizontal Asymptotes: None

Logarithmic Function (Natural) Calculator: y1= ln(x) Domain: x > 0 or x  (0,∞) Range: y   or y  (-∞,∞) Zeros: (1,0) or x = 1 X-Intercept: (1,0) Y-Intercept: none

Logarithmic Function (Natural) Symmetry: None Max: None Min: None Increasing: x  (0,∞) Decreasing: Never Vertical Asymptotes: x = 0 Horizontal Asymptotes: None

Things I should Know about Logarithmic Functions The output of a log function is an exponent. Log and exp. functions are inverses. Domain: (0, ) Range: (-, ) x-intercept of the graph: (1,0) Vertical Asymptote at x = 0 (or the y-axis)