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The logarithm of $21952$ to the base of $2 \sqrt{7}$ and $19683$ to the base of $3 \sqrt{3}$ are

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Important Questions on Exponents and Powers

MEDIUM

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

x = y^{a}

y = z^{b}

and

z = x^{c}

, then the value of

a b c

is:

EASY

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

What is the number of digit in

2^{40}

? (Given that

\log_{10} 2 = 0.301

)

EASY

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

What is the unit digit in the expansion of

67^{32}

EASY

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

What is the value of

\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{a - c} + x^{b - c}}

Where

x \neq 0

EASY

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

To what power

- 3

should be raised to get

- 2187 ?

MEDIUM

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

a = x y^{p - 1}, b = y z^{q - 1}, c = z x^{r - 1}

, then

a^{q - r} \times b^{r - p} \times c^{p - q}

is equal to:

MEDIUM

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

Which of the following pair of numbers is the solution of the equation

3^{x + 2} + 3^{- x} = 10 ?

EASY

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

Solve

\frac{2^{8} - 1}{{(\sqrt{2})}^{12}} = ?

EASY

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

{(x^{5} \div x^{4})}^{3} \div x^{2} = ?

MEDIUM

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

Determine the greatest number among the following four numbers

EASY

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

What is the number of digits in

7^{25}

8^{23}

and

9^{20}

respectively? [Given

\log_{10} (2) = 0.301

\log_{10} (3) = 0.477

\log_{10} (7) = 0.845

]

HARD

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

x^{2 a} = y^{2 b} = z^{2 c} \neq 0

and

x^{2} = y z

, then value of

\frac{a b + b c + c a}{b c}

is:

EASY

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

4^{x} . 8^{y} = 128

and

\frac{3^{x}}{27^{y}} = \frac{1}{3}

, then find the values of

x

and

y

MEDIUM

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

a^{x} = b^{y} = c^{z}

and

a b c = 1

, then the value of

\frac{1}{x} + \frac{1}{y} + \frac{1}{z}

will be equal to:

EASY

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

Find the value of '

a

' from the following

{(\sqrt{9})}^{- 5} \times {(\sqrt{3})}^{- 7} = {(\sqrt{3})}^{- a}

MEDIUM

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

{[\frac{9^{(n + \frac{1}{4})} \sqrt{3 \cdot 3^{n}}}{3 \sqrt{3^{- n}}}]}^{\frac{1}{n}} =

MEDIUM

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

Find the value/values of x for the given equation.

$2^{(2 x + 3)} - 17 = 9 (2^{x} - 2)$

MEDIUM

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

\log 2, \log (2^{x} - 1)

and

\log (2^{x} + 3)

are in

A . P .

, then

x

is equal to _________

MEDIUM

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

What is the remainder when we divide

5^{70} + 7^{70}

74

HARD

General Test>Quantitative Reasoning>Exponents and Powers>Exponents

A = 4^{5} \times 7^{3}

and

B = 7^{2} \times 4^{6}

, then what is the value of

A \times B

The logarithm of 21952 to the base of 27 and 19683 to the base of 33 are

Important Questions on Exponents and Powers

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The logarithm of $21952$ to the base of $2 \sqrt{7}$ and $19683$ to the base of $3 \sqrt{3}$ are