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PRODUCT QUOTIENT POWER
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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!
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y3 = log b x Rewrite each expression as a single logarithm 2. log 4 3 + 2log 4 x + 3log 4 y log 4 3 + log 4 x 2 + log 4 y 3 log 4 (3x 2 y 3 ) Note we are simplifying not solving for x!
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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!
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y3 = log b x Find the value of x in each logarithmic equation log 3 16 + 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.
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y3 = log b x SOLVE for x in each logarithmic equation log 3 3 = log 3 x – log 3 35.
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y3 = log b x log 4 27 – (2log 4 6 – log 4 81)=log 4 x SOLVE for x in each logarithmic equation 6.
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Solve for x: 7. 8. But x = – 6 is not in the reasonable domain
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Special Logarithm Values log a a x =___ log a b x =_____ x x xlog a b Change to logChange to exp log power rule
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y = log b x Find the inverse of each function 9. y = log 7 x 3 x = 3log 7 y
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y = log b x Find the inverse of each function 10. 11. 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
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Look above at the parent function of y = log x Domain: ________ Range: _________ V. Asymptote: _______ All reals y Parent Function Y=log x XY 0.1 10 101 3 1 10 y = x
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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.
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A. -36 B. 3 C. 6 D. 28
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A. 28 B. 30 C. 60 D. 75
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A. 3 B. 4 C. 19 D. 29
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A. 1 B. 3 C. 1/3 D. 0
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A. 3 B. 6 C. 9 D. 81
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A. -36 B. 3 C. 6 D. 28
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A. 1 B. 2 C. 9 D. 20
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A. 1/5 B. 2 C. 32 D. 10
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A. -27 B. -4 C. 9 D. 27
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A. 3 B. 5 C. 2/3 D. 30
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