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}
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}
Express in exponential form.
\displaystyle
\begin{array}{llllllll}
t = \log_5r
\end{array}
Describe the transformations of the parent function y = \log x that result in f(x).
\displaystyle
y = 2\log x - 4
Describe the transformations of the parent function y = \log x that result in f(x).
\displaystyle
y = -\log 3x
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
Describe the transformations of the parent function y = \log x that result in f(x).
\displaystyle
y= \log(x + 5) + 1
Describe the transformations of the parent function y = \log x that result in f(x).
\displaystyle
y= 5\log(-x) -3
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.
State the coordinates of the image point of (9, 2) for each of the transformed functions in question 4.
How does the graph of f(x) =2\log_2x +2 compare with the graph of g(x) = \log_2x?
Evaluate
\displaystyle
\log_381
Evaluate
\displaystyle
\log_4 \frac{1}{16}
Evaluate
\displaystyle
\log_51
Evaluate
\displaystyle
\log_{\frac{2}{3}} \frac{27}{8}
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}
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}
Express as a single logarithm.
\displaystyle
\log 7+ \log 4
Express as a single logarithm.
\displaystyle
\log 5 - \log 2
Express as a single logarithm.
\displaystyle
\log_311 + \log_34 -\log _36
Express as a single logarithm.
\displaystyle
\log_pq + \log_pq
Evaluate
\displaystyle
\log_{11}33 -\lgo_{11}3
Evaluate
\displaystyle
\log_714 + \log_73.5
Evaluate
\displaystyle
\log_5100 + \log_5 \frac{1}{4}
Evaluate
\displaystyle
\log_{\frac{1}{2}}72 - \log_{\frac{1}{2}}9
Evaluate
\displaystyle
\log_4\sqrt[3]{16}
Evaluate
\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.