Logarithms · Mathematics · NDA

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MCQ (Single Correct Answer)

1
If $${\log _8}m + {\log _8}{1 \over 6} = {2 \over 3}$$, then m is equal to
NDA 2015 Paper 2
2
If $$x + {\log _{10}}(1 + {2^x}) = x{\log _{10}}5 + {\log _{10}}6$$ then x is equal to
NDA 2017 Paper 2
3
What is the value of $${\log _7}{\log _7}\sqrt {7\sqrt {7\sqrt 7 } } $$ equal to?
NDA 2018 Paper 2
4
What is the value of $${\log _9}27 + {\log _8}32$$ ?
NDA 2018 Paper 2
5
If $${(0.2)^x} = 2$$ and $${\log _{10}}2 = 0.3010$$, then what is the value of x to the nearest tenth?
NDA 2018 Paper 2
6
If $$n = (2017)!$$, then what is $${1 \over {{{\log }_2}n}} + {1 \over {{{\log }_3}n}} + {1 \over {{{\log }_4}n}} + ... + {1 \over {{{\log }_{2017}}n}}$$ equal to?
NDA 2018 Paper 1
7
If $$x + {\log _{15}}(1 + {3^x}) = x{\log _{15}}5 + {\log _{15}}12$$, where x is an integer, then what is x equal to?
NDA 2018 Paper 1
8
If 0 < a < 1, the value of log10 a is negative. This is justified by
NDA 2018 Paper 1
9
If $${x^{{{\log }_7}x}} > 7$$ where x > 0, then which one of the following is correct?
NDA 2019 Paper 2
10
If $\log _b a=p, \log _d c=2 p$ and $\log _f e=3 p$, then what is $(a c e)^{\frac{1}{p}}$ equal to ?
NDA Mathematics 21 April 2024
11

What is the number of solutions of $\log_4(x - 1) = \log_2(x - 3)$?

NDA Mathematics 21 April 2024
12

For $x \geq y > 1$, let $\log_x\left( \frac{x}{y} \right) + \log_y\left(\frac{y}{x}\right) = k$, then the value of $k$ can never be equal to :

NDA Mathematics 21 April 2024
13
What is the minimum value of the function f(x) = log10(x2 + 2x + 11) ?
NDA Mathematics 4 September 2022
14
If f(x) = ln (x + $\sqrt{1+\text{x}^2}$), then which one of the following is correct ?
NDA Mathematics 4 September 2022
15
A radioactive substance decays at a rate proportional to the amount of substance present. If half of the substance decays in 100 years, then what is the decay constant (proportionality constant) ?
NDA Mathematics 10 April 2022
16
The value of x, satisfying the equation  $log_{cos x} ~sin x = 1$, where $0<x<\dfrac{\pi}{2}$, is
NDA Mathematics 18 April 2021
17

If n = 100!, then what is the value of the following?

$\rm \dfrac{1}{log_2n}+\dfrac{1}{log_3n}+\dfrac{1}{log_4n}+{.....}+\dfrac{1}{log_{100}n}$

NDA Mathematics 18 April 2021
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