1. Logarithms A logarithm find an exponent for a value that is not an integer. For example we know 2 x = 4 that x = 2 or 3 x = 81 x = 4, but what about … …. 4 x = 10 what is x? We would find this by writing the problem log 4 10 = x, this is read as log base 4 of 10. The general definition is log b y = x if and only if b x = y

2. The first thing we must be able to do is change from logarithmic form to exponential form and vice versa. Like 2 + 3 = 5 can change to 5 – 3 = 2 b b b b x : exp y: result

3. Change the following exponential equation to a logarithmic equation Change the following logarithmic equation to an exponential equation

4. Now that we know how to change a logarithmic equation into a exponential equation we can evaluate logarithmic functions. Write it as an exponent problem then figure out what exponent for the given base would make the answer use negative exponents to make fractions and fractional exponents to make a smaller answer. Since we know that 2 to the fifth power is 32 the answer is 5 Since we know that any number to the first power is itself then the answer is 1 Since we know that any number to the zero power is 1 then the answer is 0

5. These are a little trickier, but if we know our exponent rules and what negative exponents and rational exponents do to the base we should be fine. Anytime you are trying to make a base become a smaller number the exponent must be a rational since that really means taking a root.

6. Rewrite the following in exponential form and then solve log 9 27