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Dear Students,
Welcome to today’s quiz! This is your opportunity to demonstrate what you’ve learned so far, so do your best. Please keep in mind that you have a maximum of 30 minutes to complete all the questions. Make sure to manage your time wisely and answer each question thoughtfully.
Good luck!
Anda telah menyelesaikan kuis sebelumnya. Oleh karena itu, Anda tidak dapat memulainya lagi.
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Pertanyaan 1 dari 10
1. Pertanyaan
1 pointsIf \(\log_{}{4.5} = p\), then \(\log_{}{0.0045} = \dotso\)
Benar
\(\log_{}{0.0045} = \log_{}{4.5\times 10^{-3}}\)
\(\log_{}{0.0045} = \log_{}{4.5} + \log_{}{10^{-3}}\)
\(\log_{}{0.0045} = p \:-\: 3\)Salah
\(\log_{}{0.0045} = \log_{}{4.5\times 10^{-3}}\)
\(\log_{}{0.0045} = \log_{}{4.5} + \log_{}{10^{-3}}\)
\(\log_{}{0.0045} = p \:-\: 3\) -
Pertanyaan 2 dari 10
2. Pertanyaan
1 points\(\log_{3}{64}\times \log_{4}{15}\:-\:\log_{3}{125}= \dotso\)
Benar
\(\log_{3}{4^3}\times \log_{4}{15}\:-\:\log_{3}{5^3}\)
\(3\cdot \log_{3}{4}\times \log_{4}{15}\:-\:\log_{3}{5^3}\)
\(3\cdot \log_{3}{15}\:-\:\log_{3}{5^3}\)
\(\log_{3}{15^3}\:-\:\log_{3}{5^3}\)
\(\log_{3}{\frac{15^3}{5^3}}\)
\(\log_{3}{(\frac{15}{5})^3}\)
\(\log_{3}{3^3}\)
\(3\)Salah
\(\log_{3}{4^3}\times \log_{4}{15}\:-\:\log_{3}{5^3}\)
\(3\cdot \log_{3}{4}\times \log_{4}{15}\:-\:\log_{3}{5^3}\)
\(3\cdot \log_{3}{15}\:-\:\log_{3}{5^3}\)
\(\log_{3}{15^3}\:-\:\log_{3}{5^3}\)
\(\log_{3}{\frac{15^3}{5^3}}\)
\(\log_{3}{(\frac{15}{5})^3}\)
\(\log_{3}{3^3}\)
\(3\) -
Pertanyaan 3 dari 10
3. Pertanyaan
1 points\(7^{\log_{49}{24}} = \dotso\)
Benar
\(7^{\log_{49}{24}} = 7^{\log_{7^2}{24}}\)
\(7^{\log_{49}{24}} = 7^{\frac{1}{2}\cdot \log_{7}{24}}\)
\(7^{\log_{49}{24}} = 7^{\log_{7}{24^{\frac{1}{2}}}}\)
\(7^{\log_{49}{24}} = 24^{\frac{1}{2}}\)
\(7^{\log_{49}{24}} = \sqrt{24}\)
\(7^{\log_{49}{24}} = \sqrt{4\times 6}\)
\(7^{\log_{49}{24}} = 2\sqrt{6}\)Salah
\(7^{\log_{49}{24}} = 7^{\log_{7^2}{24}}\)
\(7^{\log_{49}{24}} = 7^{\frac{1}{2}\cdot \log_{7}{24}}\)
\(7^{\log_{49}{24}} = 7^{\log_{7}{24^{\frac{1}{2}}}}\)
\(7^{\log_{49}{24}} = 24^{\frac{1}{2}}\)
\(7^{\log_{49}{24}} = \sqrt{24}\)
\(7^{\log_{49}{24}} = \sqrt{4\times 6}\)
\(7^{\log_{49}{24}} = 2\sqrt{6}\) -
Pertanyaan 4 dari 10
4. Pertanyaan
1 points\(2^{\log_{}{5}}\:-\:5^{\log_{}{2}} = \dotso\)
Benar
\(2^{\log_{}{5}}\:-\:5^{\log_{}{2}}\)
\(2^{\log_{}{5}}\:-\:(\frac{10}{2})^{\log_{}{2}}\)
\(2^{\log_{}{5}}\:-\:\dfrac{10^{\log_{}{2}}}{2^{\log_{}{2}}}\)
\(\dfrac{2^{\log_{}{5}}\cdot 2^{\log_{}{2}}\:-\:2}{2^{\log_{}{2}}}\)
\(\dfrac{2^{\log_{}{10}}\:-\:2}{2^{\log_{}{2}}}\)
\(\dfrac{0}{2^{\log_{}{2}}}\)
\(0\)Salah
\(2^{\log_{}{5}}\:-\:5^{\log_{}{2}}\)
\(2^{\log_{}{5}}\:-\:(\frac{10}{2})^{\log_{}{2}}\)
\(2^{\log_{}{5}}\:-\:\dfrac{10^{\log_{}{2}}}{2^{\log_{}{2}}}\)
\(\dfrac{2^{\log_{}{5}}\cdot 2^{\log_{}{2}}\:-\:2}{2^{\log_{}{2}}}\)
\(\dfrac{2^{\log_{}{10}}\:-\:2}{2^{\log_{}{2}}}\)
\(\dfrac{0}{2^{\log_{}{2}}}\)
\(0\) -
Pertanyaan 5 dari 10
5. Pertanyaan
1 points\(\log_{0.5}{25}\times \log_{343}{0.125} \times \log_{25}{49} = \dotso\)
Benar
\(\log_{\frac{1}{2}}{5^2}\times \log_{7^3}{\frac{125}{1000}} \times \log_{5^2}{7^2}\)
\(\log_{2^{-1}}{5^2}\times \log_{7^3}{\frac{1}{8}} \times \log_{5^2}{7^2}\)
\(\log_{2^{-1}}{5^2}\times \log_{7^3}{2^{-3}} \times \log_{5^2}{7^2}\)
\(\frac{2}{-1}\cdot \frac{-3}{3} \cdot \frac{2}{2}\cdot \log_{2}{5}\times \log_{7}{2}\times \log_{5}{7}\)
\(2\cdot \log_{2}{5}\times \log_{5}{7}\times \log_{7}{2}\)
\(2\cdot \log_{2}{2}\)
\(2\)Salah
\(\log_{\frac{1}{2}}{5^2}\times \log_{7^3}{\frac{125}{1000}} \times \log_{5^2}{7^2}\)
\(\log_{2^{-1}}{5^2}\times \log_{7^3}{\frac{1}{8}} \times \log_{5^2}{7^2}\)
\(\log_{2^{-1}}{5^2}\times \log_{7^3}{2^{-3}} \times \log_{5^2}{7^2}\)
\(\frac{2}{-1}\cdot \frac{-3}{3} \cdot \frac{2}{2}\cdot \log_{2}{5}\times \log_{7}{2}\times \log_{5}{7}\)
\(2\cdot \log_{2}{5}\times \log_{5}{7}\times \log_{7}{2}\)
\(2\cdot \log_{2}{2}\)
\(2\) -
Pertanyaan 6 dari 10
6. Pertanyaan
1 points\((\sqrt[4]{49})^{1 + \log_{4}{64}} = \dotso\)
Benar
\((\sqrt[4]{49})^{1 + \log_{4}{64}} = (7^{\frac{2}{4}})^{1 + \log_{4}{4^3}}\)
\((\sqrt[4]{49})^{1 + \log_{4}{64}} = (7^{\frac{2}{4}})^{1 + 3}\)
\((\sqrt[4]{49})^{1 + \log_{4}{64}} = (7^{\frac{2}{\cancel{4}}})^{\cancel{4}}\)
\((\sqrt[4]{49})^{1 + \log_{4}{64}} = 49\)Salah
\((\sqrt[4]{49})^{1 + \log_{4}{64}} = (7^{\frac{2}{4}})^{1 + \log_{4}{4^3}}\)
\((\sqrt[4]{49})^{1 + \log_{4}{64}} = (7^{\frac{2}{4}})^{1 + 3}\)
\((\sqrt[4]{49})^{1 + \log_{4}{64}} = (7^{\frac{2}{\cancel{4}}})^{\cancel{4}}\)
\((\sqrt[4]{49})^{1 + \log_{4}{64}} = 49\) -
Pertanyaan 7 dari 10
7. Pertanyaan
1 pointsIf \(\log_{2}{5} = p\), then \(\log_{}{125} = \dotso\)
Benar
\(\log_{}{125} = \dfrac{\log_{5}{125}}{\log_{5}{10}}\)
\(\log_{}{125} = \dfrac{\log_{5}{5^3}}{\log_{5}{2\times 5}}\)
\(\log_{}{125} = \dfrac{\log_{5}{5^3}}{\log_{5}{2}+\log_{5}{5}}\)
\(\log_{}{125} = \dfrac{3}{\frac{1}{p} + 1}\)
\(\log_{}{125} = \dfrac{3p}{1 + p}\)Salah
\(\log_{}{125} = \dfrac{\log_{5}{125}}{\log_{5}{10}}\)
\(\log_{}{125} = \dfrac{\log_{5}{5^3}}{\log_{5}{2\times 5}}\)
\(\log_{}{125} = \dfrac{\log_{5}{5^3}}{\log_{5}{2}+\log_{5}{5}}\)
\(\log_{}{125} = \dfrac{3}{\frac{1}{p} + 1}\)
\(\log_{}{125} = \dfrac{3p}{1 + p}\) -
Pertanyaan 8 dari 10
8. Pertanyaan
1 pointsIf \(\log_{}{1.5} = p\), then \(\log_{}{0.3375} = \dotso\)
Benar
\(\log_{}{0.3375} = \log_{}{\frac{3.375}{10}}\)
\(\log_{}{0.3375} = \log_{}{3.375} \:-\: \log_{}{10}\)
\(\log_{}{0.3375} = \log_{}{(1.5)^3} \:-\: 1\)
\(\log_{}{0.3375} = 3\cdot\log_{}{1.5} \:-\: 1\)
\(\log_{}{0.3375} = 3p\:-\: 1\)Salah
\(\log_{}{0.3375} = \log_{}{\frac{3.375}{10}}\)
\(\log_{}{0.3375} = \log_{}{3.375} \:-\: \log_{}{10}\)
\(\log_{}{0.3375} = \log_{}{(1.5)^3} \:-\: 1\)
\(\log_{}{0.3375} = 3\cdot\log_{}{1.5} \:-\: 1\)
\(\log_{}{0.3375} = 3p\:-\: 1\) -
Pertanyaan 9 dari 10
9. Pertanyaan
1 points\(\dfrac{\log_{}{x\sqrt{y}} + \log_{}{y\sqrt{x}}}{\log_{}{x} + \log_{}{y}}= \dotso\)
Benar
\(\dfrac{\log_{}{x\sqrt{y}\cdot y\sqrt{x}}}{\log_{}{xy}}\)
\(\dfrac{\log_{}{x^{\frac{3}{2}\cdot y^{\frac{3}{2}}}}}{\log_{}{xy}}\)
\(\dfrac{\log_{}{(xy)^{\frac{3}{2}}}}{\log_{}{xy}}\)
\(\dfrac{3}{2}\)Salah
\(\dfrac{\log_{}{x\sqrt{y}\cdot y\sqrt{x}}}{\log_{}{xy}}\)
\(\dfrac{\log_{}{x^{\frac{3}{2}\cdot y^{\frac{3}{2}}}}}{\log_{}{xy}}\)
\(\dfrac{\log_{}{(xy)^{\frac{3}{2}}}}{\log_{}{xy}}\)
\(\dfrac{3}{2}\) -
Pertanyaan 10 dari 10
10. Pertanyaan
1 pointsIf \(\log_{2}{5} = \frac{1}{m}\) and \(\log_{2}{3} = n\), then \(\log_{40}{675} = \dotso\)
Benar
\(\log_{40}{675} = \dfrac{\log_{2}{675}}{\log_{2}{40}}\)
\(\log_{40}{675} = \dfrac{\log_{2}{3^3\cdot 5^2}}{\log_{2}{2^3\cdot 5}}\)
\(\log_{40}{675} = \dfrac{\log_{2}{3^3} + \log_{2}{5^2}}{\log_{2}{2^3} + \log_{2}{5}}\)
\(\log_{40}{675} = \dfrac{3\cdot \log_{2}{3} + 2\cdot \log_{2}{5}}{3\cdot \log_{2}{2} + \log_{2}{5}}\)
\(\log_{40}{675} = \dfrac{3n + 2\cdot\frac{1}{m}}{3 + \frac{1}{m}}\)
\(\log_{40}{675} = \dfrac{3mn + 2}{3m + 1}\)Salah
\(\log_{40}{675} = \dfrac{\log_{2}{675}}{\log_{2}{40}}\)
\(\log_{40}{675} = \dfrac{\log_{2}{3^3\cdot 5^2}}{\log_{2}{2^3\cdot 5}}\)
\(\log_{40}{675} = \dfrac{\log_{2}{3^3} + \log_{2}{5^2}}{\log_{2}{2^3} + \log_{2}{5}}\)
\(\log_{40}{675} = \dfrac{3\cdot \log_{2}{3} + 2\cdot \log_{2}{5}}{3\cdot \log_{2}{2} + \log_{2}{5}}\)
\(\log_{40}{675} = \dfrac{3n + 2\cdot\frac{1}{m}}{3 + \frac{1}{m}}\)
\(\log_{40}{675} = \dfrac{3mn + 2}{3m + 1}\)