Test 5:  Logarithms, logarithmic and radical equations

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MQ6 TEST 5A  (answers below)                                                                                      Mr. Gary Jaye

INSTRUCTIONS:   1. CALCULATORS needed.  2. Use pen.
                                  3. Express all answers in simplest form and SHOW   WORK when requested.

1. In a - g, fill in all the answers. [5, 4, 3 off for first 3 wrong answers]
In #a- c, fill in the three Pythagorean identities.
a. b. c.
In d- e, state the two standard equations of the unit circle, center at origin.
d. e.
f. In simplest form, the equivalent expression for is:
g. The transformation that maps the graph of y = bx onto the graph of y = (1/b)x is:

 

 h. When the graph of y = bx is reflected over the line defined by y = x, the equation of the image is y = _________________ .

(Answer must be in y = ??? form.)

 

 

 

 

 

 

 

 

 


2. In a - e, fill in all the answers. [3 each]
a. If logbA = 0, then A equals:
b. The characteristic of log(a.aa x 10n), where a.aa x 10n is in scientific notation form, is:
c. If the mantissas of logA and logC are equal, A and C have the same:
d. If logA - logC = 3, then A/C equals:
e. Expressed in terms of logbA, the equivalent of logb(1/A) is:

 

 

 

 

 

 


3. Express in simplest radical form. (show work). [3, 3 for first two wrong answers]
a. c.
b. d.

 

 

 

 

 

4. Answers must be EXACT.
a. Radical form only. Show sketch. [8]

 

 

 c. Cos-1(- 1/2) In radian measure. [4]

 

 

 
b. sin[Sin-1(2/7)] [2]

 

 d. Sin-1[sin(4p /3)] In radian measure. [2]

 

 

 

 

 

 

 


 

5. SHOW WORK.
a. Simplify and express result in scientific notation. [4]

(7.5 x 105)(3.0 x 10-8) 
        1.5 x 10-6

 

 

 

 Scrap area.

 

 

 

 

 

 

 

 

 

 

 

 

 

6. In a- d, you are to solve for N by using logs. Your algebra must show how you used logs to solve for N or for log N.
a. Solve for N to nearest ten thousandth: log5177 = N. [4]

 

 

 
b. Solve for N to nearest ten thousandth: 123N = 87,423 [9]

 

 

 
c. Solve for N to nearest integer: log60N = 3.2174 [9]

 

 

 
d. Solve for N to nearest hundredth: logN65536 = - 8 [9]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



7. Find number of years of annual compounding at 9.3% needed to increase original principal of $6000 to     $30,000. Assume that no contributions other than interest are made to the account. Answer (a) to      nearest hundredth, and (b) to appropriate year. [16]

 

 

 

 

 

 

 

 

 

 

 

ANSWERS:  1. See answers for 1 from previous test.   2a. A = 1   2b. characteristic = n   2c. A and C have same
significant digits   2d. A/C = 1000   2e. logb(1/A) = - logbA   3a.    3b. ap   3c. Ö (5)/5   3d. see 2e from previous test
4a. -Ö (3)/2   4b. 2/7   4c. Cos-1(-1/2) = 2p /3   4d. -p /3   5. 1.5 x 104    6a. N = log5 177 = log 177 / log 5 = 3.2161
6b. 123N = 87423 implies that log1287423 = 3N. Therefore, 3N = log1287423 = log87423 / log 12 and
N = log87423 / 3log 12 = 1.5264.   6c. log60N = 3.2174 implies that logN / log60 = 3.2174.
Therefore logN = 3.2174log60 = 5.7210 and N = 105.7210 = 526046   6d. logN65536 = - 8 implies that
log 65536 / log N = - 8. Therefore log N = (- 1/8)log 65536 = - 0.6020... and N = 10-0.6020... = .25  
7a. to nearest hundredth: 18.10   7b. appropriate year: 19

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