Rewrite each logarithm in exponential form.
1) \(\log_7\;49 = 2\)
2) \(\log_x\;27 = 3\)
3) \(\log_{\Large\frac{1}{6}}216 = -3\)
4) \(\log_{\large{n}}\;10 = 16\)
5) \(\ln_{\LARGE\frac{a}{z}}\normalsize t = -j\)
Rewrite each exponential in logarithmic form.
6) \(2^{18} = 324\)
7) \(11^{-2} = \Large\frac{1}{121}\)
8) \(\left(\Large\frac{5}{4}\right)^{-3} = \Large\frac{64}{125}\)
9) \((5.3)^{-2} = \Large\frac{100}{2809}\)
10) \(11^{-n} = \Large\frac{p}{q}\)
Evaluate each expression.
11) \(\log_4\Large\frac{1}{64}\)
12) \(\log 0.00001\)
13) \(\ln \;e^{17}\)
14) \(\log_5\;(125\cdot625)\)
15) \(\log_3\left(\Large\frac{6561}{243}\right)\)
Expand or contract each logarithmic expression.
16) \(\log_{7}\;(6x)\)
17) \(\ln_\;\Big(\Large\frac{x^2}{10}\Big)\)
18) \(\log_a\sqrt[5]{r^3}\)
19) \(\log_a\sqrt[3]{\Large\frac{r^4}{t^5}}\)
20) \(\log_4(x) - \log_4(y)\)
21) \(\log_{5}(x) + 2\log_{5}(x) - \log_{5}(y)\)
22) \(4\log_b(r) - 5\log_b(t)\)
23) \(\Large\frac{1}{3}\normalsize{\ln (x)} + \Large\frac{2}{3}\normalsize{\ln (y) - \ln (xy)}\)
Review
24) You invest \(\$330\) in money market account which pays \(3.85\%\) interest per year compounded monthly. What will be the value of the investment after \(6\) years? Round answer to the nearest cent.
25) Describe the transformations from the parent graph for \(h(x) = -3^{(x - 1)} + 7\).
26) What is the sum of all the solutions to \(\sqrt{j(j - 5)} = 6\)?
27) Let \(g(x) = x^2 - 5\). If \(f(g(x)) = \sqrt{x^{2} + 4}\), what is \(f(x)\)?
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