Свойства логарифмов | Mathematics Quiz

Свойства логарифмов

10th grade

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Mathematics

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10 hours ago

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Preview (27 questions)Show answers

Question 1
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Q.
$\log_a\left(x\cdot y\right)$
answer choices
$\log_ax\cdot\log_ay$
$\log_ax+\log_ay$
 <math><semantics><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>x</mi><mo>⋅</mo><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>y</mi></mrow><annotation encoding="application/x-tex">\log_ax\cdot\log_ay</annotation></semantics></math>logax⋅logay 
alternatives
 <math><semantics><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>x</mi><mo>+</mo><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>y</mi></mrow><annotation encoding="application/x-tex">\log_ax+\log_ay</annotation></semantics></math>logax+logay 
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Question 2
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Q.
$\log_a\left(\frac{x}{y}\right)$
answer choices
$\frac{\log_ax}{\log_ay}$
$\log_ax-\log_ay$
 <math><semantics><mrow><mfrac><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>x</mi></mrow><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>y</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{\log_ax}{\log_ay}</annotation></semantics></math>logaylogax 
alternatives
 <math><semantics><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>x</mi><mo>−</mo><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>y</mi></mrow><annotation encoding="application/x-tex">\log_ax-\log_ay</annotation></semantics></math>logax−logay 
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Question 3
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$\log_ax^b$
answer choices
$b\cdot\log_ax$
$\frac{\log_ax}{b}$
 <math><semantics><mrow><mi>b</mi><mo>⋅</mo><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>x</mi></mrow><annotation encoding="application/x-tex">b\cdot\log_ax</annotation></semantics></math>b⋅logax 
alternatives
 <math><semantics><mrow><mfrac><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>x</mi></mrow><mi>b</mi></mfrac></mrow><annotation encoding="application/x-tex">\frac{\log_ax}{b}</annotation></semantics></math>blogax 
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Question 4
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$\log_{a^b}x$
answer choices
$b\cdot\log_ax$
$\frac{\log_ax}{b}$
 <math><semantics><mrow><mi>b</mi><mo>⋅</mo><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>x</mi></mrow><annotation encoding="application/x-tex">b\cdot\log_ax</annotation></semantics></math>b⋅logax 
alternatives
 <math><semantics><mrow><mfrac><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>x</mi></mrow><mi>b</mi></mfrac></mrow><annotation encoding="application/x-tex">\frac{\log_ax}{b}</annotation></semantics></math>blogax 
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Question 5
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Q.
$\log_xy$
answer choices
$\frac{\log_ay}{\log_ax}$
$\frac{\log_ax}{\log_ay}$
$\frac{\log_xa}{\log_ay}$
$\frac{\log_ay}{\log_xa}$
 <math><semantics><mrow><mfrac><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>y</mi></mrow><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>x</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{\log_ay}{\log_ax}</annotation></semantics></math>logaxlogay 
alternatives
 <math><semantics><mrow><mfrac><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>x</mi></mrow><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>y</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{\log_ax}{\log_ay}</annotation></semantics></math>logaylogax 
 <math><semantics><mrow><mfrac><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>x</mi></msub><mi>a</mi></mrow><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>y</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{\log_xa}{\log_ay}</annotation></semantics></math>logaylogxa 
 <math><semantics><mrow><mfrac><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>y</mi></mrow><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>x</mi></msub><mi>a</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{\log_ay}{\log_xa}</annotation></semantics></math>logxalogay 
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Question 6
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$\log_xy$
answer choices
$\frac{1}{\log_yx}$
$\frac{1}{\log_ay}$
$\frac{1}{\log_xa}$
 <math><semantics><mrow><mfrac><mn>1</mn><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>y</mi></msub><mi>x</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{\log_yx}</annotation></semantics></math>logyx1 
alternatives
 <math><semantics><mrow><mfrac><mn>1</mn><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>y</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{\log_ay}</annotation></semantics></math>logay1 
 <math><semantics><mrow><mfrac><mn>1</mn><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>x</mi></msub><mi>a</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{\log_xa}</annotation></semantics></math>logxa1 
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Question 7
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Как называется процесс нахождения логарифма?
answer choices
потенцирование
логарифмирование
потенцирование
alternatives
логарифмирование
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Question 8
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Укажите правильно записанное свойство «логарифм произведения»
answer choices
$\log_an+\log_am=\log_an\cdot m$
$\log_an-\log_am=\log_an\cdot m$
$\log_an+\log_am=\log_an\div m$
 <math><semantics><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>n</mi><mo>+</mo><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>m</mi><mo>=</mo><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>n</mi><mo>⋅</mo><mi>m</mi></mrow><annotation encoding="application/x-tex">\log_an+\log_am=\log_an\cdot m</annotation></semantics></math>logan+logam=logan⋅m 
alternatives
 <math><semantics><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>n</mi><mo>−</mo><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>m</mi><mo>=</mo><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>n</mi><mo>⋅</mo><mi>m</mi></mrow><annotation encoding="application/x-tex">\log_an-\log_am=\log_an\cdot m</annotation></semantics></math>logan−logam=logan⋅m 
 <math><semantics><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>n</mi><mo>+</mo><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>m</mi><mo>=</mo><msub><mo><mi>log</mi><mo>⁡</mo></mo><mi>a</mi></msub><mi>n</mi><mo>÷</mo><mi>m</mi></mrow><annotation encoding="application/x-tex">\log_an+\log_am=\log_an\div m</annotation></semantics></math>logan+logam=logan÷m 
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Question 9
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Найдите значение логарифма $\log_232+\log_327-\log_33$
answer choices
7
8
3
7
alternatives
8
3
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Question 10
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Найдите значение выражения $\log_3\left(\left(3\log_28\right)\right)$
answer choices
1
2
3
1
alternatives
2
3
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Question 11
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Найдите значение выражения $2^{2\log_22}$
answer choices
3
4
5
3
alternatives
4
5
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Question 12
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$\log_3\ \frac{1}{81}=$
answer choices
-4
-2
-3
-4
alternatives
-2
-3
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Question 13
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$\log_4\log_381=$
answer choices
0,5
$\frac{1}{3}$
1
3
0,5
alternatives
 <math><semantics><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{3}</annotation></semantics></math>31 
1
3
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Question 14
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Q.
$\log_{\frac{1}{3}}81=$
answer choices
27
9
- 4
4
27
alternatives
9
- 4
4
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Question 15
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Q.
$Найти\ \log_672,\ если\ \log_62=а,\ \log_63=b$
answer choices
3a + 2b
2a + 3b
a - b
a + b
3a + 2b
alternatives
2a + 3b
a - b
a + b
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Question 16
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$\lg2\left(\log_220+\log_23-\log_26\right)=$
answer choices
2
0,5
1
- 1
2
alternatives
0,5
1
- 1
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Question 17
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Найти значение выражения:
log₁₆log₈64
answer choices
2
3/2
0,25
4
2
alternatives
3/2
0,25
4
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Question 18
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Q. Вычислите: log_√2(2√3 -4) + log_√2(2√3 + 4)
answer choices
4√3
решений нет
4
-4
4√3
alternatives
решений нет
4
-4
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Question 19
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Q.
Вычислите
answer choices
1
2
3
4
1
alternatives
2
3
4
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Question 20
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Q.
Основание логарифма должно быть
answer choices
а>0
a<0
a≠1
a<0, a≠1
a>0, a≠1
а>0
alternatives
a<0
a≠1
a<0, a≠1
a>0, a≠1
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Question 21
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3log₂3-log₂54
answer choices
1
-1
2
1/2
1
alternatives
-1
2
1/2
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Question 22
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Q. Найти log₄ (64/m), если log₄m=-7
answer choices
10
3/7
-3/7
-4
10
alternatives
3/7
-3/7
-4
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Question 23
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Q. Вычислите значение выражения:25^{log₅8 - log₅2 + log₅3}
answer choices
24
12
144
81
24
alternatives
12
144
81
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Question 24
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Можно ли решить , используя формулу перехода к новому основанию $\frac{\log_564}{\log_516}$
answer choices
нет
да
нет
alternatives
да
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Question 25
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Вычисли $\log_30,5+\log_94$
answer choices
$\log_32$
0
$\log_94$
другой ответ
 <math><semantics><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mn>3</mn></msub><mn>2</mn></mrow><annotation encoding="application/x-tex">\log_32</annotation></semantics></math>log32 
alternatives
0
 <math><semantics><mrow><msub><mo><mi>log</mi><mo>⁡</mo></mo><mn>9</mn></msub><mn>4</mn></mrow><annotation encoding="application/x-tex">\log_94</annotation></semantics></math>log94 
другой ответ
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Question 26
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Вычислите $\log_{\frac{1}{3}}4+\log_{27}64$
answer choices
не знаю
$2\log_{\frac{1}{3}}4$
0
4
не знаю
alternatives
 <math><semantics><mrow><mn>2</mn><msub><mo><mi>log</mi><mo>⁡</mo></mo><mfrac><mn>1</mn><mn>3</mn></mfrac></msub><mn>4</mn></mrow><annotation encoding="application/x-tex">2\log_{\frac{1}{3}}4</annotation></semantics></math>2log314 
0
4
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Question 27
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Верно ли, что $\log_{10}17=\lg17\ \ ?$
answer choices
не знаю
да
нет
не знаю
alternatives
да
нет
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