Today our topic of discussion is Exponents and Logarithm Exercises 4.3.
Exponents and Logarithm Exercises 4.3
Exercises 4.3
- On what condition a ^ 0 =1?
1) a = 0
2) a ne0
3) a > 0
4) a ne1
- Which one of the following is the value of root(5, 3) * root(5, 3) :
1) root(5, 6)
2) (root(5, 3)) ^ 3
3) (sqrt(5)) ^ 3
4) root(25, 3)
- On what exact condition log_a(a) =1?
1) a > 0
2) a ne1
3) a > 0 ,a ne1
4) a ne0,a>1
- If log_x(4) = 2 what is the value of x?
1) 2
2) plus/minus 2
3) 4
4) 10
- Under what condition can a number be written in the form a * 10 ^ n
1) 1 < a < 10
2) 1 <= a <= 10
3) 1 <= a < 10
4) 1 < a <= 10
- If a > 0 b > 0 and a ne1, b ne1 then
(i) log_a(b) * log_b(a) = 1
(ii) log_a(M ^ r) = M * log_a(r)
(iii) log_a(root(a, 3) * sqrt(a)) = 5/6
Which of the above information are correct?
1) i
2) ii
3) i and iii
4) ii and iii
- What is the characteristic of the common log of 0.0035?
1) 3
2) 1
3) 2
4) 3
Considering the number 0.0225 answer the following questions (8-10):
- Which one of the following is in the form a ^ n ?
1) (2.5) ^ 2
2) (0.015) ^ 2
3) (1.5) ^ 2
4) (0.15) ^ 2
- Which one of the following is the scientific form of the number?
1) 225 * 10 ^ – 4 2) 22.5 * 10 ^ – 3 3) 2.25 * 10 ^ – 2 4) 0.225 * 10 ^ – 1
- What is the characteristic of the common log of the number?
1) 2
2) I
3) 0
4) 2
- Express into scientific form:
1) 6530
2) 60.831
3) 0.000245
4) 37500000
5) 0.00000014
- Express in ordinary decimals: 1) 10 ^ 5
2) 10 ^ – 5
3) 2.53 * 10 ^ 4
4) 9.813 * 10 ^ – 3
5) 3.12 * 10 ^ – 5
- Find the characteristics of common logarithm of the following numbers (without using calculator) :
1) 4820
2) 72.245
3) 1.734
4) 0.045
5) 0.000036
- Find the characteristics and mantissa of the common logarithm of the following numbers by using calculator:
1) 27
2) 63.147
3) 1.405
4) 0.0456
5) 0.000673
- Find the common logarithm of the product/quotient (approximate value upto five decimal places) :
1) 5.34 * 8.7 4) 0.19926/32.4
2) 0.79 * 0.56
3) 22.2642/3.42
- If log2= 0.30103 log(3) = 0.47712 and log(7) = 0.8541 find the value of the following expressions:
1) log9
2) log(28)
3) log(42)
- Given, x = 1000 and y = 0.0625
1) Express z in the form a ^ n * b ^ n where a and b are prime numbers.
2) Express the product of x and y in scientific form.
3) Find the characteristic and mantissa of the common logarithm of xy.
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