Exponential and Logarithmic

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Presentation transcript:

Exponential and Logarithmic Practice Quest 1

1)Graph y = 5 x - 2 + 3 1. Inc/Dec Inc 2. Hor/Vert; Key Point 3. Domain: D:  4. Range: R: (3, ∞) 5. Equation of asymp. y = 3 y x 5 -5

2)Graph y = log .3 (x) – 1 1. Inc/Dec Dec 2. Hor/Vert; Key Point 1↓; (1, -1) 3. Domain: D: (0, ∞) 4. Range: R:  5. Equation of asymp. x = 0 y x 5 -5

Graph y = log e (x – 5) + 2 1. Inc/Dec Inc 2. Hor/Vert; Key Point 3. Domain: D: (5, ∞) 4. Range: R:  5. Equation of asymp. x = 5 y x 5 -5

Get same bases; set exponents =

Get same bases; set exponents =

If y = b x , then log b y = x logbaseanswer =exp, baseexp = answer 12) log 27 x = 1/3 271/3 = x (3 3)1/3= x x = 3 13) logx64= 3/2 x3/2 = 64 (x3/2)2/3 = (26)2/3 x = 24 x = 16 14) log e e5 = x e5 = ex x = 5 9) log 3 243 = x 3 x = 243 3 x = 35 x = 5 10) log264 = x 2x = 64 2x = 26 x = 6 11) log 7 1 = x 7x = 1 x = 0

If y = b x , then log b y = x logbaseanswer =exp, baseexp = answer log3 27 = x (3½)x = 33 ½x = 3 x = 6 log x5 = 1/3 x1/3 = 5 (x1/3)3 = 53 x = 125 15) log 5 x = - 4 5-4 = x x = 1/625 16) log x ¼ = -2/3 x -2/3 = ¼ (x-2/3)-3/2 = (2-2)-3/2 x = 23 x = 8 log5x = 0 50 = x x = 1

log 8 3 x2y 17) Expand ( )( log 8 + log 8 ) ( )( log 8 x + log 8 y )

log 5 (x2y)/ 2c 18)Expand log 5 x + log 5 y – log 5 2– log5 c log 5 + log 5 – log 5 – log5 log 5 x + log 5 y – log 5 2– log5 c 2log5 x +½log5 y – log5 2– log5 c

19)Write as one log: log 7y – 2log x + ½ log c log (7yc ) x2

20) Write as one log: (1/3)(log 2x2 + log 3y) log ( 6x2y) log (36x2y)