### Find the value of each of the following. Leave your answers as fractions where appropriate. Do not change bases

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A+ SOLUTIONS FOR THE FOLLOWING QUESTIONS

**Law of Exponents**

Unit Summatives

Law of Exponents Unit Assignment

Summative: Law of Exponents Unit Assignment

1.Find the value of each of the following. Leave your answers as fractions where appropriate. Do not change bases. (4 marks)

a.

b.10-10log3

c.2log39

d.log332x

2.Write the expression as a logarithm of a single quantity. (4 marks)

a.

b.

3.Write an expression for the following using a sum, difference and/or multiple of logarithms. (4 marks)

a.

b.

4.Complete the following:

a.Find the slope of the secant to the curve f(x) = -2logx + 3 between: (1 each)

i.x = 1 and x = 2

ii.x = 1 and x = 1.5

iii.x = 1 and x = 1.1

iv.x = 1 and x = 1.01

b.Extend the result from part a to determine the slope of the tangent to the curve at x = 1 accurate to 3 decimal places. (2 marks)

5.Determine the value of each of the following logarithmic expressions. Do not change bases. (2 marks)

a.log84

b.

6.Solve for x in the following equations. (4 marks)

a.log3(x - 5) + log3(x + 3) = 2

b.log7x + log7(x - 1) = log72x

7.Show that the following statement is true. (4 marks)

8.For the curve y = log(x+3), determine the following: (6 marks)

a.the asymptotes, if any

b.the intercepts, if any

c.the domain and range

9.A quantity of oxygen gas had 16.32 g of the radioactive isotope oxygen-19 in it. When measured exactly 10 minutes later, the amount of oxygen-19 was 0.964 g. What is the half-life, in seconds, of oxygen-19? (3 marks)

10.The value, V, of a $25000 vehicle after y years is given by V = 25000 (0.85)y

a.What is the rate of depreciation? (1 mark)

b.What will the car be worth after 5 years? (1 mark)

c.To the nearest month, how long would it take to reduce the vehicles value to 10% of its original amount? (3 marks)

11.Beginning with the function f(x) = logax, state what transformations were used on this to obtain the functions given below: (6 marks)

a.p(x) = - ? logax

b.r(x) = loga(5 - x)

c.t(x) = 2 loga2x

12.Give an example of a logarithmic equation that cannot be solved and explain why it cannot be solved. (3 marks)

13.Is log35 equal to log53? Explain your answer. Do not evaluate the logarithms. (2 marks)

14.The strongest recorded earthquake in the world took place in Chile on May 22 1960. It had a magnitude of 9.5 on the Richter scale. The strongest quake actually recorded in Canada was magnitude 8.1 on August 22 1949 and occurred off the Queen Charlotte Islands. (The strongest quake ever in Canada, estimated to be magnitude 9.0, happened on the west coast on January 26 1700, killing hundreds of First Nations people. We know the date because the resulting tsunami devastated the Japanese coastline.)

a.How many times more powerful was the Chilean quake than the Queen Charlotte quake? (2 marks)

b.If an earthquake only half as strong as the Queen Charlotte one were to happen today, what would its magnitude be? (3 marks)

15.State the product law for logarithms. Is it possible to use the product law for logarithms to evaluate the expression log(-7) + log(-4)? Explain your answer. (2 marks)

16.Describe the steps you would say over the telephone to explain how to solve the equation log3x + log3(x + 2) = 1 (2 marks)

17.Samir wants to invest the $10 000 lottery prize he won and let it earn interest until it became $1 million. The best long-term interest rate he could get is 5% per year. He calculated it would take about 94 years for the money to become $1 million. Deciding he couldnt wait that long, he put it into a deposit that he would take out when it became half of that, that is when it was worth $500 000. How many years did Samir have to wait? (3 marks)

18.Jacob had told Anderson to take ear protection when he went to his rock concert. Anderson said he looked up sound levels at concerts on the Internet. He saw that a conversation was rated at 60 dB and a rock concert at 120 dB. He explained to Jacob that the concert was only twice as loud as the conversation they were having. What did Jacob say in response to Andersons claim? (2 marks)

19.Describe the changes to the graph of y = log4x when x is replaced by 16x2 (3 marks)

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