CBSE Questions for Class 11 Commerce Applied Mathematics Logarithm And Antilogarithm Quiz 8 - MCQExams.com

If $$a=\log_35 $$ and $$b= \log_725$$ then correct option is:
  • $$a < b$$
  • $$ a > b$$
  • $$a= b$$
  • None of these
$$\dfrac{8^{-1}\times 5^3}{2^{-4}\times 625}=$$
  • $$\dfrac{5}{2}$$
  • $$\dfrac{2}{5}$$
  • $$25$$
  • $$5$$
Multiple Correct:
Which of the following statements are true
  • $$\log _{ 2 }{ 3 } <\log _{ 12 }{ 10 } $$
  • $$\log _{ 6 }{ 5 } <\log _{ 7 }{ 8 } $$
  • $$\log _{ 3 }{ 26 } <\log _{ 2 }{ 9 } $$
  • $$\log _{ 16 }{ 15 } >\log _{ 10 }{ 11 } >\log _{ 7 }{ 6 }$$
If the approximate value of $$ \log _{ 10 }{ (4.04) }$$is $$\ abcdef,$$ it is given that $$\log _{ 10 }{ (4) }=0.6021$$ &$$ \log _{ 10 }{ (e) }=0.4343,$$ then the value of abcd must be
  • $$6064$$
  • $$6063$$
  • $$6065$$
  • N.O.T
If $$\log_{10}e=0.4343$$, then $$\log_{10}1016$$ is
  • $$2.99$$
  • $$3$$
  • $$3.006949$$
  • $$3.02$$
The number of zeroes after decimal and before first significant digit in $$(50)^{-100}$$ is equal to : (take $$log_{10}$$ 5=0.699)
  • 168
  • 169
  • 170
  • 171
Find the value of $$\log_{10}{\left(0.\bar{9}\right)}$$
  • $$0$$
  • $$1$$
  • $$-1$$
  • $$2$$
If $$\log 4=1.3868$$, then the approximate value of $$\log\, (4.01)$$
  • $$1.3968$$
  • $$1.3898$$
  • $$1.3893$$
  • $$1.9338$$
The equation $$\log_{e}x+\log_{e}(1+x)=0$$ can be written as 
  • $$x^{2}+x-e=0$$
  • $$x^{2}+x-1=0$$
  • $$x^{2}+x+1=0$$
  • $$x^{2}+xe-e=0$$
The logarithmic form of $$4 = 2^2$$ is
  • $$ log_{ 2 }^{ 4 }= 2$$
  • $$ log_{ 2 }^{ 2 }= 2$$
  • $$ log_{ 2 }^{ 4 }=4$$
  • None of these
If $$x=500,y=100$$ and $$z=5050$$, then the value of $$(\log _{ xyz }{ { x }^{ z } } )(1+\log _{ x }{ yz } )$$ is equal to.
  • 500
  • 100
  • 5050
  • 10
The greatest value of $$(4\log_{10}{x}-\log_{x}{(0.0001)})$$ for $$0 < x < 1$$ is
  • $$4$$
  • $$-4$$
  • $$8$$
  • $$-8$$
The value of $$ 3 ^{log_4 5} -5 ^{log_4 3}$$
  • $$0$$
  • $$1$$
  • $$2$$
  • None of these
The number of $$\log_2 7 $$ is 
  • an integer
  • a rational number
  • an irrational number
  • a prime number
The value of $$0.2^{log_{\sqrt{5}} \Big( \dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{16} + \dots \Big)}$$ is
  • $$4$$
  • $$log 4$$
  • $$log 2$$
  • none of these
The value of $$\frac { \log _{ 2 }{ 24 }  }{ \log _{ 96 }{ 2 }  } -\frac { \log _{ 2 }{ 192 }  }{ \log _{ 12 }{ 2 }  } $$ is:
  • 3
  • 0
  • 2
  • 1
$$(-4)^{4}\times (4)^{1}=(4)^{5}$$
  • True
  • False
$$\left(\dfrac{2}{3}\right)^{2}\times \left(\dfrac{2}{3}\right)^{5}=\left(\dfrac{2}{3}\right)^{10}$$
  • True
  • False
$$a\times a\times b\times b\times b$$ can be written as 
  • $$a^2b^3$$
  • $$a^3b^2$$
  • $$a^3b^3$$
  • $$a^5b^5$$
$$\left(-\dfrac{8}{2}\right)^{0}=0$$
  • True
  • False
$$(-7)^{4}\times (-7)^{2}=(-7)^{6}$$
  • True
  • False
$$(-5)^{2}\times (-5)^{3}=(-5)^{6}$$
  • True
  • False
$$\left(\dfrac {1}{10}\right)^0$$ is equal to
  • $$0$$
  • $$\dfrac {1}{10}$$
  • $$1$$
  • $$10$$
By solving $$(6^0 -7^0) \times (6^0+7^0)$$, we get ________.
  • $$1$$
  • $$0$$
  • $$2$$
  • $$-1$$
If $$x$$ be any integer different from zero and $$m,n$$ be any integers then $$({x^m})^n$$ is equal 
  • $$x^{m+n}$$
  • $$x^{mn}$$
  • $$\dfrac {m}{x^n}$$
  • $$x^{m-n}$$
State whether the following statement is true (T) or false (F):
$$5^0 \times 3^0 = 8^0$$
  • True
  • False
$$\log_{\sqrt{2}} x = 4$$ then value of $$x$$ will be
  • $$4\sqrt{2}$$
  • $$\frac{1}{4}$$
  • $$4$$
  • $$4*\sqrt{2}$$
The value of $$\log (1 + 2 * 3)$$:
  • $$2\log3$$
  • $$\log1.\log.2+\log3$$
  • $$\log1+\log2+\log3$$
  • $$\log7$$
Number $$\log_{2} 7$$ is:
  • Integer
  • Rational
  • Irrational
  • Prime
$$\log_{x} 243 = 2.5$$, then value of $$x$$ will be:
  • $$9$$
  • $$3$$
  • $$1$$
  • $$81$$
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