Mid Chapter Review
Chapter
Chapter 8
Section
Mid Chapter Review
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} 

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} 

Q2

Express in exponential form.

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

Q2d

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

\displaystyle y = 2\log x - 4 

Q3a

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

\displaystyle y = -\log 3x 

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 

Q3c

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

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

Q3e

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

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

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.

Q4

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

Q5

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

Q6

Evaluate

\displaystyle \log_381 

Q7a

Evaluate

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

Q7b

Evaluate

\displaystyle \log_51 

Q7c

Evaluate

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

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} 

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} 

Q9

Express as a single logarithm.

\displaystyle \log 7+ \log 4 

Q10a

Express as a single logarithm.

\displaystyle \log 5 - \log 2 

Q10b

Express as a single logarithm.

\displaystyle \log_311 + \log_34 -\log _36 

Q10c

Express as a single logarithm.

\displaystyle \log_pq + \log_pq 

Q10d

Evaluate

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

Q11a

Evaluate

\displaystyle \log_714 + \log_73.5 

Q11b

Evaluate

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

Q11c

Evaluate

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

Q11d

Evaluate

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

\displaystyle \log_3 9\sqrt{27} 
Describe how the graph of f(x) = \log x^3 is related to the graph of g(x) = \log x.