1. LOGARITHMS

2. Find the inverse function for each of the functions below. 1.f(x) = 3x – 1 2. 3. f(x) = 2 x

3. Logarithms If f(x) = a x is a proper exponential function, then the inverse of f(x), denoted by f -1 (x), is given by f -1 (x) = log a x. (We read this, f(x) equals log base a of x) If b a = c, then a = log b (c) If (base) exponent = answer, then log base (answer) = exponent Exponential formLogarithmic form 5 3 = 125 2 -3 = 1/8 log 3 (27) = 3 log 9 (1/81) = -2

4. Rewrite into each logarithmic equation in exponential form and mentally confirm they are true. 1.log 10 (100) = 2 2.log 2 (64) = 6 3. log 9 (27) = 3/2 4. log 10 (1/10) = -1

5. Evaluate each of the following. Try not to use a calculator. 1.log 4 (16) 2.log 3 (81) 3.log 10 (10 5/8 ) 4. log 2 (32)

6. Common Logarithm A logarithm with a base of 10 is called a common logarithm. log 10 (a) = log (a) Natural Logarithm A logarithm with a base of e is called a natural logarithm. log e (a) = ln (a)

7. Evaluate each of the following using your calculator. Round your answer to three decimal places. 1.log 9 2.ln 4 3.log 10 2 4. log 10 3 5. log 10 -1 6. ln e 2 7. ln e 3 8. ln e -4 Do you see a pattern in #3 - 8

8. Something interesting about logs: log b b x = x Something interesting about exponents:

9. Evaluate the following. Each problems should take 2 seconds. 1.log 3 (3 7 ) = 2. log 13 (13 x+2 ) = 3. 4.

10. Find the value of the variable in each of the following equations. (Hint: Rewrite in exponential form) 1.log 5 (x) = 4 2.log b (125) = 3 3.log 8 (x) = 5/3 4. log b (27) = 3/2

11. Graph y = 2 x and y = log 2 x State the domain, range and equation of asymptote of each. How are the graphs related?

12. For each of the following: a.State the transformations b.State the domain, range and equation of asymptote c.Make a sketch 1.y = 3 x – 2 2.y = log 4 (x + 1) 3.f(x) = 4 (x – 2) + 1 4. f(x) = -ln x + 3

13. Find the inverse for each of the following functions. 1.f(x) = log 4 x 2. f(x) = log x 3. f(x) = 8 x 4. f(x) = e x