တက္ကသိုလ်ဝင်တန်း မေးခွန်းမှာ MCQ Format မပါတော့ပေမယ့် Multiple Choice Question ဆိုတာ ကျောင်းသားရဲ့ ဘာသာရပ်ဆိုင်ရာ နားလည်တတ်သိမှု၊ ဖြတ်ထိုးဉာဏ်၊ ဆင်ခြင်နိုင်စွမ်း စတာတွေကို စစ်ဆေးတာဖြစ်လို့ လေ့ကျင့်ထားသင့်ပါတယ်။ နိုင်ငံတကာ တက္ကသိုလ်ဝင် စာမေးပွဲများမှာလည်း MCQ ကိုပဲ ဦးစားပေး မေးလေ့ရှိတာမို့ နိုင်ငံရပ်ခြား ကျောင်းတက်ဖို့ စာမေးပွဲဖြေဆိုမည့်သူများ အတွက်လည်း အသုံးဝင်ပါလိမ့်မယ်။
Definition: Logarithm
Let $N$ and $b$ be positive real numbers, with $b \neq 1$. Then the logarithm of $N$ (with respect) to the base $b$ is the exponent by which $b$ must be raised to yield $N$, and is denoted by $\log _{b} N$
Rules of Logarithms
$\begin{array}{ll} \text{L}1. & N=b^{\log _{b} N}\\\\ \text{L}2. & x=\log _{b} b^{x}\\\\ \text{L}3. & \log _{b} b=1\\\\ \text{L}4. & \log _{b} 1=0\\\\ \text{L}5. & \log _{b}(M N)=\log _{b} M+\log _{b} N\\\\ \text{L}6. & \log _{b} N^{p}=p \log _{b} N\\\\ \text{L}7. & \log _{b}\left(\displaystyle\frac{M}{N}\right)=\log _{b} M-\log _{b} N\\\\ \text{L}8. & \log _{a} N=\displaystyle\frac{\log _{b} N}{\log _{b} N}\\\\ \text{L}9. & \log _{a} N=\displaystyle\frac{1}{\log _{N} a}\\\\ \text{L}10. & \log _{a^{p}} N=\displaystyle\frac{1}{p} \log _{a} N\\\\ \text{L}11. & a^{\log _{k} b}=b^{\log _{k} a} \end{array}$
Common Logarithm
The logarithm of $N$ to the base $10\left(\log _{10} N\right)$ is said to be a common logarithm, and is usually written as $\log N$ (omitting the base). where $n$ is called the characteristic and $\log a$ is called the mantissa of $\log N$.
If $\quad N=a \times 10^{n}$,
then $\quad \log N=\log \left(a \times 10^{n}\right)=\log 10^{n}+\log a=n+\log a$ where $n$ is called the characteristic and $\log a$ is called the mantissa of $\log N$.
Note that $n$ is an integer and $1 \leq a<10$
Euler's Number
As a positive integer $n$ become very large, the value of $\left(1+\displaystyle\frac{1}{n}\right)^{n}$ approaches an irrational number, which is denoted by $e$.
Natural Logarithm
The logarithm of $N$ to the base $e$ is called a natural logarithm, and is denoted by $\ln N$.
MCQ Test
| 1. | If $\log _{10} x=3$ then $x=$ A. $500$ B. $\displaystyle\frac{10}{3}$ C. $700$ D. $ 1000$ |
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| 2. | If $\log _{7} x=2$, then $x=$ A. $14$ B. $49$ C. $128$ D. $64$ |
| 3. | The characteristic of log 19 is A. $0$ B. $10$ C. $2$ D. $ 1$ |
| 4. | The characteristic of $\log 3.216$ is A. $0$ B. $4$ C. $3$ D. $10$ |
| 5. | Common logarithm has the base A. $2$ B. $e$ C. $\pi$ D. $ 10$ |
| 6. | In scientific notation $0.00416$ is written as A. $0.0416 \times 10^{-1}$ B. $0.416 \times 10^{-2}$ C. $ 4.16 \times 10^{-3}$ D. $41.6 \times 10^{-4}$ |
| 7. | In decimal form $2.35 \times 10^{-2}$ is written as A. $2.35$ B. $0.0235$ C. $0.00235$ D. $0.000235$ |
| 8. | $\log 5+\log 8-\log 3=$ A. $5 \log \displaystyle\frac{8}{3}$ B. $3 \log 40$ C. $\log \displaystyle\frac{40}{3}$ D. $3 \log \displaystyle\frac{5}{8}$ |
| 9. | $\log 50$ can be written as A. $\log 2+2 \log 5$ B. $\log 2+\log 15$ C. $\log 2+5\log 2$ D. $\log 2+\log 5$ |
| 10. | 3 is the characteristic in the logarithm of the number A. $879.2$ B. $87.92$ C. $8.792$ D. $8792$ |
| 11. | If $\log _{2} 8=x$ then $x=$ A. $2^{8}$ B. $64$ C. $3^{2}$ D. $3$ |
| 12. | $5^{4}=625$ is written in the logarithmic form as A. $\log 5=625$ B. $\log _{5} 4=625$ C. $\log _{5} 625=4$ D. $\log _{4} 625=5$ |
| 13. | If $\log _{81} x=-\displaystyle\frac{3}{4}$ then $x=$ A. $27$ B. $\displaystyle\frac{1}{3}$ C. $\displaystyle\frac{1}{27}$ D. $\displaystyle\frac{1}{9}$ |
| 14. | If antilog $3.8716=7440$ and $\log x=0.8716$ then $x=$ A. $74.40$ B. $7.440$ C. $744.0$ D. $7440$ |
| 15. | If $\log 5=0.6990$ and $\log 3=0.4771$, then $\log 45=$ A. $1.6532$ B. $1.1761$ C. $1.8751$ D. $1.2219$ |
| 16. | 3 log2 $-2$ log5 in the simplified form is A. $\log \displaystyle\frac{6}{10}$ B. $\log \displaystyle\frac{9}{12}$ C. $\log \displaystyle\frac{8}{25}$ D. $\log \displaystyle\frac{25}{8}$ |
| 17. | If $\log _{x} 81=4$ then $x=$ A. $3$ B. $2$ C. $-1$ D. $0$ |
| 18. | If $\log _{8} x=\displaystyle\frac{2}{3}$ then $x=$ A. $2$ B. $4$ C. $3$ D. $-1$ |
| 19. | $3 \log 2+\log 3=\log x$ then $x=$ A. $12$ B. $18$ C. $24$ D. $30$ |
| 20. | If $\log _{4} 64=x$, then $x=$ A. $2$ B. $-1$ C. $0$ D. $3$ |
| 21. | If $\log _{81} 9=x$, then $x=$ A. $3$ B. $2$ C. $1$ D. $\displaystyle\frac{1}{2}$ |
| 22. | If $\log_{x} 49=2 ; x=$ A. $6$ B. $3$ C. $7$ D. $0$ |
| 23. | If $\log 35+\log 36=\log (3 x)$ then $x=$ A. $400$ B. $420$ C. $520$ D. $600$ |
| 24. | $\log 3+\log 6-\log 2=\log x$ then $x=$ A. $10$ B. $9$ C. $8$ D. $7$ |
| 25. | $\log_{x} 36=2$ then $x=$ A. $5$ B. $8$ C. $2$ D. $6$ |
| 26. | If $\log_{8} 16=x$, then $x=$ A. $\displaystyle\frac{4}{3}$ B. $\displaystyle\frac{1}{2}$, C. $2$ D. $-\displaystyle\frac{1}{2}$ |
| 27. | $\log 5+\log 8-\log 6=$ A. $\log 7$ B. $\log \displaystyle\frac{13}{6}$ C. $\log \displaystyle\frac{40}{6}$ D. $\log 50$ |
| 28. | The characteristic of $\log 0.00329$ is A. $\overline{1}$ B. $\overline{3}$ C. $\overline{2}$ D. $0$ |
| 29. | The characteristic of $\log 1.02$ is A. $1$ B. $\overline{3}$ C. $0$ D. $-1$ |
| 30. | If $\log _{10} 100=x$, then $x=$ A. $2$ B. $1$ C. $0$ D. $-1$ |
| 31. | The characteristic of $\log 0.000753$ is A. $\overline{1}$ B. $\overline{2}$ C. $\overline{3}$ D. $\overline{4}$ |
| 32. | The exponential form of $y=\log _{a} x$ is A. $ x=y$ B. $a^{y}=x$ C. $x^{y}=a$ D. $a=x^{y}$ |
| 33. | The logarithmic form of $a=y^x$ is A. $\log _{a} x=y$ B. $ \log _{y} a=x$ C. $\log _{x} y=a$ D. $\log _{a} y=x$ |
| 34. | The integral part of logarithm is called A. determinant B. matrix C. mantissa D. characteristic |
| 35. | The decimal part of logarithm is called A. determinant B. set C. mantissa D. characteristic |
| 36. | $ \displaystyle\frac{\log 5}{\log 3}=$ A. $\log 5-\log 3$ B. $\log_{3} 5$ C. $\log_{5} 3$ D. $\log\displaystyle\frac{ 5}{3}$ |
| 37. | $\log 729=$ A. $\log 3$ B. $6 \log 3$ C. $\log 6$ D. $\log 3+\log 6$ |
| 38. | If $\log 2=0.3010 . \log 3=0.4771, \log 5=0.6990$ then $\log 30=$ A. $1.4771$ B. $0.4771$ C. $-0.4771$ D. $-1.4771$ |
| 39. | If $\log 2=0.3010, \log 3=0.4771$ then $\log 4.5=$ A. $0.7781$ B. $0.1761$ C.$0.6532$ D. $1.6532$ |
| 40. | If $\log _{10} 7=a$, then $\log _{10}\left(\displaystyle\frac{1}{70}\right)=$ A. $-(1+a)$ B. $\displaystyle\frac{1}{1+a}$ C. $\displaystyle\frac{a}{10}$ D. $\displaystyle\frac{1}{10 a}$ |
| 41. | $\displaystyle\frac{1}{\log _{a} b} \times \displaystyle\frac{1}{\log _{b} c} \times \displaystyle\frac{1}{\log _{c} a}=$ A. $-1$ B. $0$ C. $1$ D. $a b c$ |
| 42. | If $\log _{10} 2=a$ and $\log _{10} 3=b$ then $\log _{5} 12=$ A. $\displaystyle\frac{a+b}{1+a}$ B. $\displaystyle\frac{2 a+b}{1+a}$ C. $\displaystyle\frac{a+2 b}{1+a}$ D. $\displaystyle\frac{2 a+b}{1-a}$ |
| 43. | If $\log _{a}(a b)=x$, then $\log _{b}(a b)=$ A. $\displaystyle\frac{1}{x}$ B. $\displaystyle\frac{x}{x+1}$ C. $\displaystyle\frac{x}{1-x}$ D. $\displaystyle\frac{x}{x-1}$ |
| 44. | $2 \log _{10} 5+\log _{10} 8-\displaystyle\frac{1}{2} \log _{10} 4=$ A. $2$ B. $4$ C. $2\left(1-\log _{10} 1\right)$ D. $4\left(1-\log _{10} 1\right)$ |
| 45. | If $\log _{5}\left(x^{2}+x\right)-\log _{5}(x+1)=2$, then $x=$ A. $5$ B. $10$ C. $25$ D. $\displaystyle\frac{1}{5}$ |
| 46. | If $\log _{10} x-5 \log _{10} 3=-2$, then $x=$ A. $\displaystyle\frac{80}{100}$ B. $\displaystyle\frac{81}{100}$ C. $\displaystyle\frac{125}{100}$ D. $\displaystyle\frac{243}{100}$ |
| 47. | If $\log _{3} x+\log _{9} x^{2}+\log _{27} x^{3}=9$, then $x=$ A. $3$ B. $9$ C. $27$ D. $\displaystyle\frac{1}{3}$ |
| 48. | If $a=\log _{8} 225$ and $b=\log _{2} 15$, then $\displaystyle\frac{a}{b}=$ A. $\displaystyle\frac{1}{3}$ B. $\displaystyle\frac{2}{3}$ C. $\displaystyle\frac{3}{2}$ D. $3$ |
| 49. | If the logarithm of a number is $-3.153$, what are characteristic and mantissa? A. characteristic $=-4, \quad$ mantissa $=0.847$ B. characteristic $=-4, \quad$ mantissa $=0.153$ C. characteristic $=4, \quad$ mantissa $=-0.847$ D. characteristic $=-3, \quad$ mantissa $=-0.153$ |
| 50. | If $\log \left(\displaystyle\frac{a}{b}\right)+\log \left(\displaystyle\frac{b}{a}\right)=\log (a+b)$, then A. $a+b=1$ B. $a-b=1$ C. $a=b$ D. $a^{2}+b^{2}=1$ |
Answer Keys
| $\begin{array}{|ll|ll|ll|ll|ll|} \hline 1. &\text {D} & 2. &\text {B} & 3. &\text {D} & 4. &\text {A} & 5. &\text {D} \\ \hline 6. &\text {C} & 7. &\text {B} & 8. & \text{C} & 9. &\text {A }& 10.&\text {D} \\ \hline 11.&\text {D} & 12.&\text {C} & 13.&\text {C} & 14.&\text {B} & 15.&\text {A} \\ \hline 16.&\text {C} & 17.&\text {A} & 18.&\text {B} & 19.&\text {C} & 20.&\text {D} \\ \hline 21.&\text {D} & 22.&\text {C} & 23.&\text {B} & 24.&\text {B} & 25.&\text {D} \\ \hline 26.&\text {A} & 27.&\text {C} & 28.&\text {B} & 29.&\text {C} & 30.&\text {A} \\ \hline 31.&\text {D} & 32.&\text {B} & 33.&\text {B} & 34.&\text {D} & 35.&\text {C} \\ \hline 36.&\text {B} & 37.&\text {B} & 38.&\text {A} & 39.&\text {C} & 40.&\text {A} \\ \hline 41.&\text {C} & 42.&\text {D} & 43.&\text {D} & 44.& \text {A}& 45.&\text {C} \\ \hline 46.&\text {D} & 47.&\text {C} & 48.&\text {B} & 49.&\text {A} & 50.&\text {A} \\ \hline \end{array}$ |
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