Logarithmic Inequalities

Solving Logarithmic Equations and Inequalities

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Not in Packet

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Kyle faster

Adam faster

Same swimming time

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Page 3 #1

About how many days after their first competition did the boys have the same swimming time, and what was that time?



These answers are estimates

Around ​

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days

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seconds

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Page 3 #2

When are Adam's times faster than Kyle's?



These answers are estimates

​

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​

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days

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Page 3 #2

When are Kyle's times faster than Adam's?



These answers are estimates

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​

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days

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Page 3 #4

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Solve the following inequality using graphs on Desmos (pictured on the side).



5-3lnx≤2+7lnx

x ​

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​

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Options (4)

Page 4 #5

Solve 1106.3 – 27.49 ln(D + 1) < 1152.8 – 35.73 ln(D + 1)

Isolate the ln

Exponentiate Both Sides

Solve

Answer

Open Ended

Page 4 #6

How does the answer from #5 compare to the answer from #1-3 you found by graphing?

Are they the same? Are they different? Is one exact? Is one an estimate?

Match

Page 5 #7 First Box

Kristi deposits $2,640 into an account that pays 3.5% interest compounded quarterly. If Kristi makes no additional deposits and does not make any withdrawals, how long will it take Kristi’s investment to be worth $6,000?

• A=

• P=

• r=

• n=

• t=

6000

2640

.035

4

?

• 6000

• 2640

• .035

• 4

• ?

Reorder

Page 5 #7 First Box

Kristi deposits $2,640 into an account that pays 3.5% interest compounded quarterly. If Kristi makes no additional deposits and does not make any withdrawals, how long will it take Kristi’s investment to be worth $6,000?

• Divide both sides by 2640 and simplify in parenthesis

• Take the log of both sides

• Use log properties to bring exponent in front of the log

• Divide by anything except the variable

• Type into Desmos

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

​Page 5 #7 First Box

Match

Page 5 #7 Second Box

A magazine notices that the number of subscriptions has been decreasing at a rate of 4.5% each year. If the magazine has 36,000 subscribers and the subscriptions continue to decrease at this rate, how long will it take for the number of subscribers to decrease by half?

• A=

• a=

• r=

• t=

18000

36000

.045

?

• 18000

• 36000

• .045

• ?

Reorder

Page 5 #7 Second Box

A magazine notices that the number of subscriptions has been decreasing at a rate of 4.5% each year. If the magazine has 36,000 subscribers and the subscriptions continue to decrease at this rate, how long will it take for the number of subscribers to decrease by half?

• Divide both sides by 36000 and simplify in parenthesis

• Take the log of both sides

• Use log properties to bring exponent in front of the log

• Divide by anything except the variable

• Type into Desmos

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

​Page 5 #7 Second Box

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Page 5 #7 Third Box

Put the steps in the correct order.

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Around 6 hours