Solve each equation.
1) \(49^x = 7\)
2) \(5^{x - 4} = 25\)
3) \(16^{2x} = \Large\frac{1}{64}\)
4) \(8^{x + 4} = 2^{2x - 12}\)
5) \(16^{x + 7} = 64^{x-2}\)
6) \(\left(\large\frac{1}{3}\right)^{2x} = \normalsize81^{x-3}\)
7) \(4^{2x + 5} = \sqrt[3]{\large\frac{1}{64}}\)
Solve each equation to the nearest hundredth.
8) \(5^{x + 1} = 50\)
9) \(12^{x - 2} = 20\)
10) \(\left(\Large\frac{1}{2}\right)^x = \normalsize11\)
Solve each equation.
11) \(\ln x = \ln (-2x + 7)\)
12) \(\log_4\;(7x + 3) = \log_4\;(5x + 9)\)
13) \(\log_5\;(x^2 - 4) = \log_5\;(5x + 10)\)
14) \(\log_7\;(x^2 + 4x) = \log_7\;(5x + 6)\)
15) \(\log_6\;(x + 2) + \log_6\;(x + 1) = \log_6\;(-4x - 10)\)
16) \(\ln x - \ln (x - 3) = \ln 2\)
17) \(\ln(5 + 4x) - \ln(3 + x) = \ln\;\frac{4}{5}\)
18) \(\log_5\;(x + 2) + \log_5\;25 = 3\)
19) \(\log_4\;(x + 2) + \log_4\;(x - 2) = 2\)
20) \(\log_3\;(11x + 9) = 2 + \log_3\;(x + 3)\)
21) Create a logarithmic equation that has a solution of \(2\) and an extraneous solution of \(-5\).
Review
22) Expand or contract the expression \(3\log(x) + \log(y) - 2\log(x)\).
23) Graph the function \(p(x) = -\log(x - 1) - 10\) and state the domain, range and vertical asymptote.
24) If \(3x − y = 12\), what is the value of \(\Large\frac{8^x}{2^y}\)?
a) \(2^{12}\)
b) \(4^4\)
c) \(8^2\)
d) not enough information
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