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Logarithms Chapter 10 Objective You will be able to define a logarithm and convert from an exponential to a log and vice versa. You will analyze basic logs and evaluate whether they exist or not. If the function cannot be solved and: … it is in Exponential Form then switch it to Logarithmic Form … it is in Logarithmic Form then switch it to Exponential Form What is a Log? A logarithm is an exponent. 2x=y is an exponential. List the Domain and the Range. Find the Inverse x = 2y y = 2x x f(x) x f(x) -2 -1 0 1 2 1/4 1/2 1 2 4 1/4 1/2 1 2 4 -2 -1 0 1 2 PLOT the coordinates on the same set of axes. Inverse Log But we can’t re-solve x = 2y for y. So mathematicians developed the logarithm as the inverse of the exponential. The Logarithm is the exponent which makes the equation (function) true. Equivalent forms. y = 2x is equal to log2 y = x. Rewrite y = 2x as 2x = y. SNAIL to change between forms. Log2 Y 2x = y Head is base of the Base > 0; Base 1 Log The answer =x Exponent Now Try to change forms Try and change more … 2