Graphs of Logs

(to me log graphs look the same as exponential graphs but rotated)

The graph of y = log_a x has the same general shape for all values of the base a where a > 1.

These type of graphs have these properties:

• curve only exists for positive values of x

• gradient is always positive, as the value of x increases the gradient decreases

• crosses the x-axis at (1,0)

• y-axis is an asymptote

• graph always passes through (a,1)

• log_a x is negative if the value of x is 0<x<1

Logarithmic functions are the inverse of exponential functions, the expression of log x = y is the same as 10^y = x, and so their graphs will be identical

Interchanging x and y for the graph ‘y = log_a x’ gives the curve ‘x = log_a y’

when your trying to make y the subject ‘x = log_a y’ → a^x = y