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Exponents and Logarithms (সূচক এবং লগারিদম)

**Exponents and Logarithms Quiz** enhances your knowledge and skills in Exponents and Logarithm problems. You will have **10** minutes to complete the quiz and if you do not answer any question within the specified time, it will be considered incorrect. You need to get a minimum of **50%** marks to pass the quiz. Press the "**Start Quiz**" button to participate in the quiz.

1 / 35

If a^{n} is an exponential expression, which is not true for n?

2 / 35

According to exponent rules, when we multiply the expressions, we _______ the exponents.

3 / 35

If a ϵ R and m, n ϵ N, then a^{m} × a^{n} =?

^{m + n}

^{m}× a

^{n}

^{a}

^{mn}

4 / 35

2^{2} × 2^{3} =?

5 / 35

According to exponent rules, when we divide the expressions, we _______ the exponents.

6 / 35

If a ϵ R and m, n ϵ N, then a^{m}/a^{n} =?

^{m – n}

^{m + n}

^{m}– a

^{n}

^{mn}

7 / 35

8^{5}/8^{3} =?

8 / 35

If a, b ϵ R and n ϵ N, then (ab)^{n}=?

^{n}× b

^{n}

^{n}- b

^{n}

^{n}× b

^{-n}

^{m}× b

^{n}

9 / 35

(7 × 4)^{2 }=?

10 / 35

If a, b ϵ R and n ϵ N, then (a/b)^{ n}=?

^{n}/b

^{n}

^{n}- b

^{n}

^{n}+ b

^{n}

^{n}× b

^{n}

11 / 35

(8/5)^{2} =?

^{2}/5

^{2}

^{2}/8

^{2}

^{2}× 5

^{2}

^{2}+ 5

^{2}

12 / 35

If a ϵ R and m, n ϵ N, then (a^{m})^{n }=?

^{mn}

^{n}

^{mn}

^{an}

13 / 35

(2^{3})^{2} =?

14 / 35

a^{0} =?

15 / 35

a^{-n} =?

^{n}

^{-n}

^{-a}

^{-a}

16 / 35

5^{-2} =?

17 / 35

Which of the following is the standard form of 0.00001275?

^{-5}

^{-5}

^{-5}

^{5}

18 / 35

Solve the equation: 2^{2x + 1} = 128.

19 / 35

Solve the equation: 2^{x} + 2^{1 - x} = 3.

20 / 35

If a, m and n are positive integers and a ≠ 1, then log_{a}(mn) =

_{a}m + log

_{a}n

_{a}m - log

_{a}n

_{a}m

_{p}m/log

_{p}n

21 / 35

If a, m and n are positive integers and a ≠ 1, then log_{a}(m/n) =?

_{a}m - log

_{a}n

_{p}m/log

_{p}n

_{a}m

_{a}m + log

_{a}n

22 / 35

If a and m are positive numbers, a ≠ 1 and r is a real number, then log_{a}m^{r} =?

_{a}m

_{p}m/log

_{p}n

_{m}n

_{a}m - log

_{a}n

23 / 35

If m, n and p are positive numbers and n ≠ 1, p ≠ 1, then; Log_{n}m =?

_{p}m/log

_{p}n

_{a}m

_{a}m - log

_{a}n

_{m}n

24 / 35

If m and n are the positive numbers other than 1, then log_{n}m =?

_{m}n

_{p}m/log

_{p}n

_{a}m

_{a}m - log

_{a}n

25 / 35

e^{ln n }=?

26 / 35

Find the value of log_{10}100.

27 / 35

Find the value of log_{3}(1/9).

28 / 35

Find the value of log_{√3}81.

29 / 35

What is the log of 5√5 to the base of 5?

30 / 35

If the log of 400 is 4, then what is the base of the log?

31 / 35

The logarithms having a base '10' are called -

32 / 35

The relation x = log_{a}n implies

^{x}= n

^{n}= x

^{x}= a

^{a}= n

33 / 35

Solve the equation: log_{x}324 = 4.

34 / 35

If log_{x}y = 100 and log_{2}x = 10, then the value of y is:

^{1000}

^{10}

^{100}

^{10000}

35 / 35

log_{10}1 =?

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