Chapter 13

1. $\begin{array}{rcl} \log_{9} x & = & - \frac{1}{2} \\ x & = & 9^{- 1/2} \\ = & \frac{1}{9^{1/2}} = \frac{1}{3} \end{array}$
2. $\begin{array}{rcl} \log_{3} x & - & \log_{3} 2 = 2 \\ \log_{3} \frac{x}{2} & = & 2 \\ \frac{x}{2} & = & 3^{2} \\ x & = & 2 (3^{2}) = 18 \end{array}$
3. $\begin{array}{rcl} \log_{x} 64 & = & 3 \\ 64 & = & x^{3} \\ 4^{3} & = & x^{3} \\ x & = & 4 \end{array}$
4. $\begin{array}{l} 3^{3 x + 1} = 8 \\ \begin{array}{rcl} (3 x + 1) \log 3 & = & \log 8 \\ 3 x + 1 & = & \frac{\log 8}{\log 3} \\ x & = & \frac{1}{3} (\frac{\log 8}{\log 3} - 1) = 0.298 \end{array} \end{array}$
5. $y = 2 \log_{4} x$

x $\frac{1}{4}$ 1 4 16

y $- 2$ 0 2 4

$\log_{4} \frac{1}{4} = - 1, \log_{4} 16 = 2$
6. $y = 2 (3^{x})$

x $- 1$ 0 1 2

y 0.7 2 6 18

x 3 4 5

y 54 162 486
7. $\begin{array}{rcl} \log_{5} (\frac{4 a^{3}}{7}) & = & \log_{5} 4 a^{3} - \log_{5} 7 \\ = & \log_{5} 4 + \log_{5} a^{3} - \log_{5} 7 \\ = & \log_{5} 4 + 3 \log_{5} a - \log_{5} 7 \\ = & 2 \log_{5} 2 + 3 \log_{5} a - \log_{5} 7 \end{array}$
8. $\begin{array}{l} 3 \log_{7} x - \log_{7} y = 2 \\ \log_{7} x^{3} - \log_{7} y = 2 \\ \begin{array}{l} \log_{7} \frac{x^{3}}{y} = 2 & \frac{x^{3}}{y} = 7^{2} \end{array} \\ \begin{array}{l} x^{3} = \end{array} \end{array}$

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Basic Technical Mathematics, 11th Edition by Allyn J. Washington, Richard Evans

`x`	$\frac{1}{4}$	1	4	16
`y`	$- 2$	0	2	4

`x`	$- 1$	0	1	2
`y`	0.7	2	6	18

`x`	3	4	5
`y`	54	162	486