PRODUCT QUOTIENT POWER y = log b x Rewrite each expression as a single logarithm 1. log 8 18 – log 8 6 log 8 log 8 3 Note we are simplifying not solving.

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Presentation transcript:

PRODUCT QUOTIENT POWER

y = log b x Rewrite each expression as a single logarithm 1. log 8 18 – log 8 6 log 8 log 8 3 Note we are simplifying not solving for x!

y3 = log b x Rewrite each expression as a single logarithm 2. log log 4 x + 3log 4 y log log 4 x 2 + log 4 y 3 log 4 (3x 2 y 3 ) Note we are simplifying not solving for x!

y3 = log b x Rewrite each expression as a single logarithm 3. log x + log x – 2 log x log log 1 Which btw means 10 0 =1 so the simplified answer is 0...but we were asked for a log Note we are simplifying not solving for x!

y3 = log b x Find the value of x in each logarithmic equation log log 3 25=log 3 x log 3 (16 25 )=log 3 x log 3 (2 5)=log 3 x log 3 (10)=log 3 x Note we are solving for x !! 4.

y3 = log b x SOLVE for x in each logarithmic equation log 3 3 = log 3 x – log 3 35.

y3 = log b x log 4 27 – (2log 4 6 – log 4 81)=log 4 x SOLVE for x in each logarithmic equation 6.

Solve for x: But x = – 6 is not in the reasonable domain

Special Logarithm Values log a a x =___ log a b x =_____ x x xlog a b Change to logChange to exp log power rule

y = log b x Find the inverse of each function 9. y = log 7 x 3 x = 3log 7 y

y = log b x Find the inverse of each function y = log(x+1) x = log(y+1) y = log(10x) 10 x = y+1 x = log(10y) 10 x =10y 10 x – 1 = y 10 (x-1) =y

Look above at the parent function of y = log x Domain: ________ Range: _________ V. Asymptote: _______ All reals y Parent Function Y=log x XY y = x

Activity: Now lets see what you know. I will show you some problems. When I ask for the answer, please show the color of the matching correct answer.

 A. -36  B. 3  C. 6  D. 28

 A. 28  B. 30  C. 60  D. 75

 A. 3  B. 4  C. 19  D. 29

 A. 1  B. 3  C. 1/3  D. 0

 A. 3  B. 6  C. 9  D. 81

 A. -36  B. 3  C. 6  D. 28

 A. 1  B. 2  C. 9  D. 20

 A. 1/5  B. 2  C. 32  D. 10

 A. -27  B. -4  C. 9  D. 27

 A. 3  B. 5  C. 2/3  D. 30