Today we did a warm-up with a liftoff function. example: g5(125)= g5(5^3)=3. Then we had to sketch y=4^x and use it to sketch a graph of a) y= 4^(-x) - 3, b) y=16*4^x and c) y=4^(0.5x). In b) 16=4^2 which makes y=4^2 + 4^x = 4^(x+2). In c) 4=2^2 which makes y= (2^2)^(0.5x)= 2^x. Then we discussed exercises 55 and 59 from hw. We used a formula A=P(1 + (r/n))^nt and GDC. Then we also used A=Pe^(rt) formula. Then we did the last page of Mystery function. Then we realized that mystery function and liftoff function is log. Definition: x=b^y means the same as y=log (b)^x. We went to http://www.purplemath.com/modules/logs.htm.
example: log(27)^9, in words: "The power you raise 27 to to get 9"
Then we found the inverse of exponential: f(x)=b^x then: y=b^x, then inverse: x=b^y, then solve for y: y= log(b)^x. So f^(-1)(x)=log (b)^x