Mid Chapter Review
Chapter
Chapter 8
Section
Mid Chapter Review
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Solutions 28 Videos

Express in log form.

\displaystyle \begin{array}{llllllll} &(a) \phantom{.} y = 5^x &(b) \phantom{.} x = 10^y \\ &(c) \phantom{.} y = (\frac{1}{3})^x &(d) \phantom{.} m = p^q \end{array} 

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Q1

Express in exponential form.

\displaystyle \begin{array}{llllllll} &(a) \phantom{.} y = \log_3x &(b) \phantom{.} y = \log x\\ &(c) \phantom{.} k = \log m \end{array} 

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Q2

Express in exponential form.

\displaystyle \begin{array}{llllllll} t = \log_5r \end{array} 

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Q2d

Describe the transformations of the parent function y = \log x that result in f(x).

\displaystyle y = 2\log x - 4 

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Q3a

Describe the transformations of the parent function y = \log x that result in f(x).

\displaystyle y = -\log 3x 

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Q3b

Describe the transformations of the parent function y = \log x that result in f(x).

\displaystyle y= \frac{1}{4}\log \frac{1}{4}x 

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Q3c

Describe the transformations of the parent function y = \log x that result in f(x).

\displaystyle y= \log(x + 5) + 1 

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Q3e

Describe the transformations of the parent function y = \log x that result in f(x).

\displaystyle y= 5\log(-x) -3 

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Q3f

Given the parent function y = \log x, write the equation of the function that results from each set of transformations.

a) vertical stretch by a factor of 4, followed by a reflection in the x-axis

b) horizontal translation 3 units to the left followed by a vertical translation 1 unit up.

c) vertical compression by a factor of \frac{2}{3}, followed by a horizontal stretch by a factor of 2.

d) vertical stretch a factor of 3, followed y a reflection in the y-axis and a horizontal translation 1 unit to the right.

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Q4

State the coordinates of the image point of (9, 2) for each of the transformed functions in question 4.

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Q5

How does the graph of f(x) =2\log_2x +2 compare with the graph of g(x) = \log_2x?

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Q6

Evaluate

\displaystyle \log_381 

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Q7a

Evaluate

\displaystyle \log_4 \frac{1}{16} 

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Q7b

Evaluate

\displaystyle \log_51 

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Q7c

Evaluate

\displaystyle \log_{\frac{2}{3}} \frac{27}{8} 

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Q7d

Evaluate the three decimal places.

\displaystyle \begin{array}{llllllll} &(a) \phantom{.} \log 4 &(b) \phantom{.} \log 45 \\ &(c) \phantom{.} \log 135 &(d) \phantom{.} \log 300 \end{array} 

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Q8

Evaluate the value of each expression to three decimal places.

\displaystyle \begin{array}{llllllll} &(a) \phantom{.} \log_221 &(b) \phantom{.} \log_5117 \\ &(c) \phantom{.} \log_7141 &(d) \phantom{.} \log_{11}356 \end{array} 

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Q9

Express as a single logarithm.

\displaystyle \log 7+ \log 4 

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Q10a

Express as a single logarithm.

\displaystyle \log 5 - \log 2 

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Q10b

Express as a single logarithm.

\displaystyle \log_311 + \log_34 -\log _36 

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Q10c

Express as a single logarithm.

\displaystyle \log_pq + \log_pq 

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Q10d

Evaluate

\displaystyle \log_{11}33 -\lgo_{11}3 

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Q11a

Evaluate

\displaystyle \log_714 + \log_73.5 

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Q11b

Evaluate

\displaystyle \log_5100 + \log_5 \frac{1}{4} 

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Q11c

Evaluate

\displaystyle \log_{\frac{1}{2}}72 - \log_{\frac{1}{2}}9 

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Q11d

Evaluate

\displaystyle \log_4\sqrt[3]{16} 

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Q11e

Evaluate

\displaystyle \log_3 9\sqrt{27} 

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Q11f

Describe how the graph of f(x) = \log x^3 is related to the graph of g(x) = \log x.

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Q12