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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!
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Pertanyaan 1 dari 20
1. Pertanyaan
1 pointsBentuk logaritma yang tidak terdefinisi adalah …
Benar
\(^a\log_{}{b}\) dengan \(a\) basis dan \(b\) numerus
1. Syarat basis, \(a > 0 \text{ dan } a \neq 1\)
2. Syarat numerus, \(b > 0\)Jadi logaritma yang tidak terdefinisi adalah \(^1\log 7\)
Salah
\(^a\log_{}{b}\) dengan \(a\) basis dan \(b\) numerus
1. Syarat basis, \(a > 0 \text{ dan } a \neq 1\)
2. Syarat numerus, \(b > 0\)Jadi logaritma yang tidak terdefinisi adalah \(^1\log 7\)
-
Pertanyaan 2 dari 20
2. Pertanyaan
1 pointsPenulisan \(10^4 = 10000\) dalam bentuk logaritma yang benar adalah …
Benar
\(a^c = b \rightarrow ^a\log_{}{b} = c\)
\(10^4 = 10000 \rightarrow ^{10}\log 10000 = 4 \text{ atau ditulis } \log 10000 = 4\)
catatan : basis 10 tidak ditulisSalah
\(a^c = b \rightarrow ^a\log_{}{b} = c\)
\(10^4 = 10000 \rightarrow ^{10}\log 10000 = 4 \text{ atau ditulis } \log 10000 = 4\)
catatan : basis 10 tidak ditulis -
Pertanyaan 3 dari 20
3. Pertanyaan
1 pointsJika \(^8\log_{}{p} = \dfrac{2}{3}\) maka nilai \(p = \dotso\)
Benar
\(^8\log_{}{p} = \dfrac{2}{3}\)
\(p = 8^{\frac{2}{3}}\)
\(p = 2^{3\times \frac{2}{3}}\)
\(p = 2^2\)
\(p = 4\)Salah
\(^8\log_{}{p} = \dfrac{2}{3}\)
\(p = 8^{\frac{2}{3}}\)
\(p = 2^{3\times \frac{2}{3}}\)
\(p = 2^2\)
\(p = 4\)Hint
\(^{\text{a}}\log_{}{\text{b}} = \text{c}\rightarrow \text{b} = \text{a}^{\text{c}}\) -
Pertanyaan 4 dari 20
4. Pertanyaan
1 pointsJika \(^a\log_{}{27} = 3\) maka nilai \(a = \dotso\)
Benar
\(^a\log_{}{27} = 3\)
\(27 = a^3\)
\(3^3 = a^3\)
\(a = 3\)Salah
\(^a\log_{}{27} = 3\)
\(27 = a^3\)
\(3^3 = a^3\)
\(a = 3\) -
Pertanyaan 5 dari 20
5. Pertanyaan
1 pointsJika \(^{64}\log y = -\frac{5}{6}\) maka nilai \(y = \dotso\)
Benar
\(^{64}\log_{}{y} = -\frac{5}{6}\)
\(^{2^6}\log_{}{y} = -\frac{5}{6}\)
\(y = (2^6)^{-\frac{5}{6}}\)
\(y = 2^{-5}\)
\(y = \frac{1}{2^5}\)
\(y = \frac{1}{32}\)Salah
\(^{64}\log_{}{y} = -\frac{5}{6}\)
\(^{2^6}\log_{}{y} = -\frac{5}{6}\)
\(y = (2^6)^{-\frac{5}{6}}\)
\(y = 2^{-5}\)
\(y = \frac{1}{2^5}\)
\(y = \frac{1}{32}\) -
Pertanyaan 6 dari 20
6. Pertanyaan
1 pointsNIlai dari \(^2\log_{}{0,125}\) adalah …
Benar
\(^2\log_{}{0,125} = ^2\log_{}{\dfrac{1}{8}}\)
\(^2\log_{}{0,125} = ^2\log_{}{\dfrac{1}{2^3}}\)
\(^2\log_{}{0,125} = ^2\log_{}{2^{-3}}\)
\(^2\log_{}{0,125} = -3\)Salah
\(^2\log_{}{0,125} = ^2\log_{}{\dfrac{1}{8}}\)
\(^2\log_{}{0,125} = ^2\log_{}{\dfrac{1}{2^3}}\)
\(^2\log_{}{0,125} = ^2\log_{}{2^{-3}}\)
\(^2\log_{}{0,125} = -3\) -
Pertanyaan 7 dari 20
7. Pertanyaan
1 points\(^7\log_{}{343} + ^2\log_{}{128}\:-\:\log_{}{1000} = \dotso\)
Benar
\(^7\log_{}{343} + ^2\log_{}{128}\:-\:\log_{}{1000}\)
\(^7\log_{}{7^3} + ^2\log_{}{2^7}\:-\:\log_{}{10^3}\)
\(3\cdot ^7\log_{}{7} + 7\cdot ^2\log_{}{2}\:-\:3\cdot \log_{}{10}\)
\(3 + 7 \:-\: 3\)
\(7\)Salah
\(^7\log_{}{343} + ^2\log_{}{128}\:-\:\log_{}{1000}\)
\(^7\log_{}{7^3} + ^2\log_{}{2^7}\:-\:\log_{}{10^3}\)
\(3\cdot ^7\log_{}{7} + 7\cdot ^2\log_{}{2}\:-\:3\cdot \log_{}{10}\)
\(3 + 7 \:-\: 3\)
\(7\) -
Pertanyaan 8 dari 20
8. Pertanyaan
1 pointsJika \(^6\log_{}{125} = k\cdot ^6\log_{}{5}\) maka nilai \(k = \dotso\)
Benar
\(^6\log_{}{125} = k\cdot ^6\log_{}{5}\)
\(^6\log_{}{5^3} = k\cdot ^6\log_{}{5}\)
\(3\cdot ^6\log_{}{5} = k\cdot ^6\log_{}{5}\)
\(k = 3\)Salah
\(^6\log_{}{125} = k\cdot ^6\log_{}{5}\)
\(^6\log_{}{5^3} = k\cdot ^6\log_{}{5}\)
\(3\cdot ^6\log_{}{5} = k\cdot ^6\log_{}{5}\)
\(k = 3\) -
Pertanyaan 9 dari 20
9. Pertanyaan
1 points\(^9\log_{}{3\sqrt{3}} = \dotso\)
Benar
\(^9\log_{}{3\sqrt{3}} = ^{3^2}\log_{}{3^{\frac{3}{2}}}\)
\(^9\log_{}{3\sqrt{3}} = \frac{\frac{3}{2}}{2}\cdot ^{3}\log_{}{3}\)
\(^9\log_{}{3\sqrt{3}} = \frac{3}{4}\cdot 1\)
\(^9\log_{}{3\sqrt{3}} = \frac{3}{4}\)Salah
\(^9\log_{}{3\sqrt{3}} = ^{3^2}\log_{}{3^{\frac{3}{2}}}\)
\(^9\log_{}{3\sqrt{3}} = \frac{\frac{3}{2}}{2}\cdot ^{3}\log_{}{3}\)
\(^9\log_{}{3\sqrt{3}} = \frac{3}{4}\cdot 1\)
\(^9\log_{}{3\sqrt{3}} = \frac{3}{4}\) -
Pertanyaan 10 dari 20
10. Pertanyaan
1 points\(^{9y}\log_{}{27y^{\frac{3}{2}}} = \dotso\)
Benar
\(^{9y}\log_{}{27y^{\frac{3}{2}}} = ^{9y}\log_{}{(9y)^{\frac{3}{2}}}\)
\(^{9y}\log_{}{27y^{\frac{3}{2}}} = \frac{3}{2}\cdot ^{9y}\log_{}{9y}\)
\(^{9y}\log_{}{27y^{\frac{3}{2}}} = \frac{3}{2}\cdot 1\)
\(^{9y}\log_{}{27y^{\frac{3}{2}}} = \frac{3}{2}\)Salah
\(^{9y}\log_{}{27y^{\frac{3}{2}}} = ^{9y}\log_{}{(9y)^{\frac{3}{2}}}\)
\(^{9y}\log_{}{27y^{\frac{3}{2}}} = \frac{3}{2}\cdot ^{9y}\log_{}{9y}\)
\(^{9y}\log_{}{27y^{\frac{3}{2}}} = \frac{3}{2}\cdot 1\)
\(^{9y}\log_{}{27y^{\frac{3}{2}}} = \frac{3}{2}\) -
Pertanyaan 11 dari 20
11. Pertanyaan
1 points\(^{x^2\cdot\sqrt{x}}\log_{}{(x^5\cdot\sqrt{x})} = \dotso\)
Benar
\(^{x^2\cdot\sqrt{x}}\log_{}{(x^5\cdot\sqrt{x})} = ^{x^{\frac{5}{2}}}\log_{}{x^{\frac{11}{2}}}\)
\(^{x^2\cdot\sqrt{x}}\log_{}{(x^5\cdot\sqrt{x})} = \frac{\frac{11}{2}}{\frac{5}{2}}\cdot ^x\log_{}{x}\)
\(^{x^2\cdot\sqrt{x}}\log_{}{(x^5\cdot\sqrt{x})} = \frac{11}{5}\cdot 1\)
\(^{x^2\cdot\sqrt{x}}\log_{}{(x^5\cdot\sqrt{x})} = 2,2\)Salah
\(^{x^2\cdot\sqrt{x}}\log_{}{(x^5\cdot\sqrt{x})} = ^{x^{\frac{5}{2}}}\log_{}{x^{\frac{11}{2}}}\)
\(^{x^2\cdot\sqrt{x}}\log_{}{(x^5\cdot\sqrt{x})} = \frac{\frac{11}{2}}{\frac{5}{2}}\cdot ^x\log_{}{x}\)
\(^{x^2\cdot\sqrt{x}}\log_{}{(x^5\cdot\sqrt{x})} = \frac{11}{5}\cdot 1\)
\(^{x^2\cdot\sqrt{x}}\log_{}{(x^5\cdot\sqrt{x})} = 2,2\) -
Pertanyaan 12 dari 20
12. Pertanyaan
1 points\(^5\log_{}{\frac{1}{5}} + \log_{}{10} + \log_{}{1} = \dotso\)
Benar
\(^5\log_{}{\frac{1}{5}} + \log_{}{10} + \log_{}{1}\)
\(^5\log_{}{5^{-1}} + 1 + 0\)
\(-1\cdot ^5\log_{}{5} + 1\)
\(-1 + 1\)
\(0\)Salah
\(^5\log_{}{\frac{1}{5}} + \log_{}{10} + \log_{}{1}\)
\(^5\log_{}{5^{-1}} + 1 + 0\)
\(-1\cdot ^5\log_{}{5} + 1\)
\(-1 + 1\)
\(0\) -
Pertanyaan 13 dari 20
13. Pertanyaan
1 points\(^9\log_{}{729} + ^{32}\log_{}{16}\:-\: ^{49}\log_{}{\frac{1}{343}} = \dotso\)
Benar
\(^9\log_{}{729} + ^{32}\log_{}{16}\:-\: ^{49}\log_{}{\frac{1}{343}}\)
\(^{3^2}\log_{}{3^6} + ^{2^5}\log_{}{2^4}\:-\: ^{7^2}\log_{}{\frac{1}{7^3}}\)
\(\frac{6}{2}\cdot ^{3}\log_{}{3} + \frac{4}{5}\cdot ^{2}\log_{}{2}\:-\: ^{7^2}\log_{}{7^{-3}}\)
\(3 + \frac{4}{5}\:-\: \frac{-3}{2}\cdot^{7}\log_{}{7}\)
\(3 + \frac{4}{5}\:-\: \frac{-3}{2}\)
\(5,3\)Salah
\(^9\log_{}{729} + ^{32}\log_{}{16}\:-\: ^{49}\log_{}{\frac{1}{343}}\)
\(^{3^2}\log_{}{3^6} + ^{2^5}\log_{}{2^4}\:-\: ^{7^2}\log_{}{\frac{1}{7^3}}\)
\(\frac{6}{2}\cdot ^{3}\log_{}{3} + \frac{4}{5}\cdot ^{2}\log_{}{2}\:-\: ^{7^2}\log_{}{7^{-3}}\)
\(3 + \frac{4}{5}\:-\: \frac{-3}{2}\cdot^{7}\log_{}{7}\)
\(3 + \frac{4}{5}\:-\: \frac{-3}{2}\)
\(5,3\) -
Pertanyaan 14 dari 20
14. Pertanyaan
1 points\(^2\log_{}{^3\log_{}{^3\log_{}{3^9}}} = \dotso\)
Benar
\(^2\log_{}{^3\log_{}{(9\cdot ^3\log_{}{3})}}\)
\(^2\log_{}{^3\log_{}{9}}\)
\(^2\log_{}{^3\log_{}{3^2}}\)
\(^2\log_{}{(2\cdot ^3\log_{}{3})}\)
\(^2\log_{}{2} = 1\)Salah
\(^2\log_{}{^3\log_{}{(9\cdot ^3\log_{}{3})}}\)
\(^2\log_{}{^3\log_{}{9}}\)
\(^2\log_{}{^3\log_{}{3^2}}\)
\(^2\log_{}{(2\cdot ^3\log_{}{3})}\)
\(^2\log_{}{2} = 1\) -
Pertanyaan 15 dari 20
15. Pertanyaan
1 points\(^3\log_{}{\log_{}{1000}} + ^5\log_{}{\log_{}{100000}} = \dotso\)
Benar
\(^3\log_{}{\log_{}{10^3}} + ^5\log_{}{\log_{}{10^5}}\)
\(^3\log_{}{(3\cdot \log_{}{10})} + ^5\log_{}{(5\cdot \log_{}{10})}\)
\(^3\log_{}{3} + ^5\log_{}{5}\)
\(1 + 1 = 2\)Salah
\(^3\log_{}{\log_{}{10^3}} + ^5\log_{}{\log_{}{10^5}}\)
\(^3\log_{}{(3\cdot \log_{}{10})} + ^5\log_{}{(5\cdot \log_{}{10})}\)
\(^3\log_{}{3} + ^5\log_{}{5}\)
\(1 + 1 = 2\) -
Pertanyaan 16 dari 20
16. Pertanyaan
1 points\(^{25}\log_{}{0,2} + ^4\log_{}{0,5} + ^2\log_{}{1} = \dotso\)
Benar
\(^{5^2}\log_{}{\frac{1}{5}} + ^{2^2}\log_{}{\frac{1}{2}} + ^2\log_{}{1}\)
\(^{5^2}\log_{}{5^{-1}} + ^{2^2}\log_{}{2^{-1}} + 0\)
\(\frac{-1}{2}\cdot ^{5}\log_{}{5} + \frac{-1}{2}\cdot ^{2}\log_{}{2}\)
\(\frac{-1}{2} + \frac{-1}{2} = -1\)Salah
\(^{5^2}\log_{}{\frac{1}{5}} + ^{2^2}\log_{}{\frac{1}{2}} + ^2\log_{}{1}\)
\(^{5^2}\log_{}{5^{-1}} + ^{2^2}\log_{}{2^{-1}} + 0\)
\(\frac{-1}{2}\cdot ^{5}\log_{}{5} + \frac{-1}{2}\cdot ^{2}\log_{}{2}\)
\(\frac{-1}{2} + \frac{-1}{2} = -1\) -
Pertanyaan 17 dari 20
17. Pertanyaan
1 points\(^{x^5}\log_{}{\sqrt{x}} + ^{x^2}\log_{}{(x^2\cdot \sqrt{x})} = \dotso\)
Benar
\(^{x^5}\log_{}{x^{\frac{1}{2}}} + ^{x^2}\log_{}{x^{\frac{5}{2}}}\)
\(\frac{\frac{1}{2}}{5}\cdot ^{x}\log_{}{x} + \frac{\frac{5}{2}}{2}\cdot ^{x}\log_{}{x}\)
\(\frac{1}{10} + \frac{5}{4}\)
\(\frac{27}{20} = 1,35\)Salah
\(^{x^5}\log_{}{x^{\frac{1}{2}}} + ^{x^2}\log_{}{x^{\frac{5}{2}}}\)
\(\frac{\frac{1}{2}}{5}\cdot ^{x}\log_{}{x} + \frac{\frac{5}{2}}{2}\cdot ^{x}\log_{}{x}\)
\(\frac{1}{10} + \frac{5}{4}\)
\(\frac{27}{20} = 1,35\) -
Pertanyaan 18 dari 20
18. Pertanyaan
1 pointsJika \(^8\log_{}{3} + ^{32}\log_{}{81} = k \cdot ^2\log_{}{3}\) maka nilai \(15k = \dotso\)
Benar
\(^{2^3}\log_{}{3^1} + ^{2^5}\log_{}{3^4} = k \cdot ^2\log_{}{3}\)
\(\frac{1}{3}\cdot ^{2}\log_{}{3} + \frac{4}{5}\cdot ^{2}\log_{}{3} = k \cdot ^2\log_{}{3}\)
\(\frac{17}{15}\cdot ^{2}\log_{}{3} = k \cdot ^2\log_{}{3}\)
\(k = \frac{17}{15}\)
\(15k = \cancel{15}\times \frac{17}{\cancel{15}} = 17\)Salah
\(^{2^3}\log_{}{3^1} + ^{2^5}\log_{}{3^4} = k \cdot ^2\log_{}{3}\)
\(\frac{1}{3}\cdot ^{2}\log_{}{3} + \frac{4}{5}\cdot ^{2}\log_{}{3} = k \cdot ^2\log_{}{3}\)
\(\frac{17}{15}\cdot ^{2}\log_{}{3} = k \cdot ^2\log_{}{3}\)
\(k = \frac{17}{15}\)
\(15k = \cancel{15}\times \frac{17}{\cancel{15}} = 17\) -
Pertanyaan 19 dari 20
19. Pertanyaan
1 points\(^{0,25}\log_{}{16} + ^{0,008}\log_{}{125} \:-\: ^{0,380}\log_{}{1} = \dotso\)
Benar
\(^{\frac{1}{4}}\log_{}{4^2} + ^{\frac{1}{125}}\log_{}{125} \:-\: ^{0,380}\log_{}{1}\)
\(^{4^{-1}}\log_{}{4^2} + ^{125^{-1}}\log_{}{125} \:-\: 0\)
\(\frac{2}{-1}\cdot ^{4}\log_{}{4} + \frac{1}{-1}\cdot ^{125}\log_{}{125}\)
\(-2 \:-\:1 = -3\)Salah
\(^{\frac{1}{4}}\log_{}{4^2} + ^{\frac{1}{125}}\log_{}{125} \:-\: ^{0,380}\log_{}{1}\)
\(^{4^{-1}}\log_{}{4^2} + ^{125^{-1}}\log_{}{125} \:-\: 0\)
\(\frac{2}{-1}\cdot ^{4}\log_{}{4} + \frac{1}{-1}\cdot ^{125}\log_{}{125}\)
\(-2 \:-\:1 = -3\) -
Pertanyaan 20 dari 20
20. Pertanyaan
1 pointsJika \(^x\log_{}{80} = ^{2x}\log_{}{10}\) maka nilai \(x = \dotso\)
Benar
\(^x\log_{}{80} = ^{2x}\log_{}{10}\)
Misal:
\(^x\log_{}{80} = k\)
\(80 = x^k\)\(^{2x}\log_{}{10} = k\)
\(10 = (2x)^k\)
\(10 = 2^k\cdot x^k\)
\(10 = 2^k\cdot 80\)
\(\frac{10}{80} = 2^k\)
\(\frac{1}{8} = 2^k\)
\(2^{-3} = 2^k\)
\(k = -3\)\(80 = x^k\)
\(80 = x^{-3}\)
\(80^{-\frac{1}{3}} = x\)
\(x = \frac{1}{\sqrt[3] {80}}\)Salah
\(^x\log_{}{80} = ^{2x}\log_{}{10}\)
Misal:
\(^x\log_{}{80} = k\)
\(80 = x^k\)\(^{2x}\log_{}{10} = k\)
\(10 = (2x)^k\)
\(10 = 2^k\cdot x^k\)
\(10 = 2^k\cdot 80\)
\(\frac{10}{80} = 2^k\)
\(\frac{1}{8} = 2^k\)
\(2^{-3} = 2^k\)
\(k = -3\)\(80 = x^k\)
\(80 = x^{-3}\)
\(80^{-\frac{1}{3}} = x\)
\(x = \frac{1}{\sqrt[3] {80}}\)