Going back to our improved tripling pizza oven that you saw in class with a dial

Question

Going back to our improved tripling pizza oven that you saw in class with a dial that replaces both the button and the switch: When they dial 4 and turn the oven on, it is like pushing the old button 4 one pizza in the oven, dial 4, and turn the oven on, they will get 81 pizzas. ( 34 81) Then if they dial -4 and turn the oven on it is like flicking the old switch four times. If they started with one whole pizza, dialed -4, and turned the oven on, they would get 1/81 of a pizza. (3-4-01 ) numbers, both positive and negative that are not integers. If they start with one whole pizza, dial 1/2 and turn the oven on, you saw in class they got about 1.73 pizzas. (32 1.73) a. If you start with 1 whole pizza, where should you set the dial, so you come out with 10 pizzas after you turn the oven on. Think about which two whole numbers to set the dial several numbers and check orn your calculator. See how close you can get to 10.

Explanation / Answer

a) we need 10 pizzas. lets assume the dial number be x.

implies, 3x= 10. we can guess that 32=9 and 33=27. So the dial should be in between 2 & 3.

if we use logarithm technique, apply logarithm on both sides of the equation.

log103x= log1010

we know,  log1010 = 1

xlog103=1

x= 1/log103= 2.096

we need to set the dail on 2.096 for exactly 10 pizzas.

b) we know, 34=81 & 35=243. so, we need 100 pizzas implies the dial should be in between 4 & 5.

if we use logarithm technique, apply logarithm on both sides of the equation.

log103x= log10100

log10100=log10102= 2log1010

we know,  log1010 = 1

xlog103=2

x= 2/log103= 4.192

c) we need 1000 pizzas, we can represent 1000 as 103 and if we follow the similar techniques as above, we get 3x2.096 = 6.288 will give 1000 pizzas.

d) we need 1/10 pizzas,  we can represent 1/10 as 10-1 and if we follow the similar techniques as above, we get -1x2.096 = -2.096 will give 11/10 pizzas.

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