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Arithmetic Ability
Logarithm
Quiz 1
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Q.1
If $$\log 3\log \left( {{3^x} - 2} \right)\,$$ and $$\log \left( {{3^x} + 4} \right)$$ are in arithmetic progression, then x is equal to
$$\frac{8}{3}$$
$$\log {3^8}$$
$$\log {2^3}$$
8
Q.2
If $${\text{a}} = {\text{lo}}{{\text{g}}_{\text{8}}}\,{\text{225}}$$ and $${\text{b = lo}}{{\text{g}}_{\text{2}}}\,{\text{15}},$$ then a in terms of b is -
$$\frac{b}{2}$$
$$\frac{{2b}}{3}$$
b
$$\frac{{3b}}{2}$$
Q.3
If $${\log _{10}}a = p,$$ $${\log _{10}}b = q,$$ then what is $${\log _{10}}\left( {{a^p}{b^q}} \right)$$ equal to?
p
2
+ q
2
p
2
- q
2
p
2
q
2
$$\frac{{{p^2}}}{{{q^2}}}$$
Q.4
If $$\log 2 = 0.3010\,$$ and $$\log 3 = 0.4771,\,$$ the value of $${\log _5}512$$ = ?
2.870
2.967
3.876
3.912
Q.5
If the logarithm of a number is - 3.153, what are characteristic and mantissa?
characteristic = -4, mantissa = 0.847
characteristic = -3, mantissa = -0.153
characteristic = 4, mantissa = -0.847
characteristic = 3, mantissa = -0.153
Q.6
If $${\log _{10}}7 = a,$$ then $${\log _{10}}\left( {\frac{1}{{70}}} \right)$$ is equal to -
-(1 + a)
(1 + a)
-1
$$\frac{a}{{10}}$$
$$\frac{1}{{10a}}$$
Q.7
If $$\log x - 5\log 3 = - 2,$$ then x equals -
0.8
0.81
1.25
2.43
Q.8
If $$\log 2 = 0.30103,$$ the number of digits in $${4^{50}}$$ is -
30
31
100
200
Q.9
The number of digits in $${{\text{4}}^9} \times {{\text{5}}^{17}}{\text{,}}$$ when expressed in usual form, is -
16
17
18
19
Q.10
$$\frac{1}{2}\left( {\log x + \log y} \right)$$ will equal to $$\log \left( {\frac{{x + y}}{2}} \right)$$ if -
y = 0
x = $$\sqrt {\text{y}} $$
x = y
x = $$\frac{{\text{y}}}{2}$$
Q.11
If $$\log \frac{a}{b} + \log \frac{b}{a} = $$ $$\,\log \left( {a + b} \right),$$ then -
a + b = 1
a - b = 1
a = b
a
2
- b
2
= 1
Q.12
If $$a = {b^2} = {c^3} = {d^4},$$ then the value of $${\log _a}\left( {abcd} \right)$$ would be -
$${\log _a}1 + {\log _a}2 + {\log _a}3 + {\log _a}4$$
$${\log _a}24$$
$${\text{1 + }}\frac{1}{2} + \frac{1}{3} + \frac{1}{4}$$
$${\text{1 + }}\frac{1}{{2!}} + \frac{1}{{3!}} + \frac{1}{{4!}}$$
Q.13
If $${\log _3}x + {\log _{9}}{x^2} + {\log _{27}}{x^3}$$ $$ = 9,$$ then x equals to -
3
9
27
None of these
Q.14
If $${\log _7}{\log _5}\left( {\sqrt {x + 5} + \sqrt x } \right)$$ $$ = 0,$$ what is the value of x ?
2
3
4
5
Q.15
If $${\log _{10000}}x = - \frac{1}{4}{\text{,}}$$ then the value of x is = ?
$$\frac{1}{{10}}$$
$$\frac{1}{{100}}$$
$$\frac{1}{{1000}}$$
$$\frac{1}{{10000}}$$
Q.16
$$\frac{{\log \sqrt 8 }}{{\log 8}}\,\,{\text{is equal to = ?}}$$
$$\frac{1}{{\sqrt 8 }}$$
$$\frac{1}{4}$$
$$\frac{1}{2}$$
$$\frac{1}{8}$$
Q.17
$${\log \left( {\frac{{{a^2}}}{{bc}}} \right) + }$$ $${\log \left( {\frac{{{b^2}}}{{ac}}} \right) + }$$ $${\log \left( {\frac{{{c^2}}}{{ab}}} \right)}$$ is equal to -
0
1
2
abc
Q.18
$$\frac{1}{{{{\log }_a}b}} \times \frac{1}{{{{\log }_b}c}} \times \frac{1}{{{{\log }_c}a}}$$ is equal to -
a + b + c
abc
0
1
Q.19
$$2{\log _{10}}^5 + $$ $${\log _{10}}8 \,- $$ $$\frac{1}{2}{\log _{10}}4$$ = ?
2
4
$${\text{2 - 2 lo}}{{\text{g}}_{10}}^2$$
$${\text{4 - 4 lo}}{{\text{g}}_{10}}^2$$
Q.20
If $${\log _a}\left( {ab} \right) = x{\text{,}}\,$$ then $${\log _b}\left( {ab} \right)$$ is -
$$\frac{1}{x}$$
$$\frac{x}{{x + 1}}$$
$$\frac{x}{{1 - x}}$$
$$\frac{x}{{x - 1}}$$
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