EASY

Earn 100

The number of zeros coming immediately after the decimal point in the value of ${(0 .2)}^{25}$ is/are (given $\log_{10} 2 = 0.30103$ )

60% studentsanswered this correctly

Important Questions on Logarithm and its Applications

MEDIUM

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

Let

n

be the smallest positive integer such that

1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n} \geq 4

. Which one of the following statements is true?

EASY

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

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

then

x =

MEDIUM

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

Let

x, y

be real numbers such that

x > 2 y > 0

and

2 \log (x - 2 y) = \log x + \log y

. Then the possible value(s) of

\frac{x}{y}

MEDIUM

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

If $\log 3^{x + 4} = \log 729$ then the value of $x$ will be

MEDIUM

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

The number of solution pairs

(x, y)

of the simultaneous equations

\log_{1 / 3} (x + y) + \log_{3} (x - y) = 2

and

2 y^{2} = 512^{x + 1}

EASY

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

\log_{e} (y^{2}) = \tan (\frac{1}{x}),

then

y =

HARD

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

The solution set of the inequality

\log_{\sin (π / 3)} (x^{2} - 3 x + 2) \geq 2

EASY

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

The number of significant figures in

50000.020 \times 10^{- 3}

HARD

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

\log_{(3 x - 1)} (x - 2) = \log_{(9 x^{2} - 6 x + 1)} (2 x^{2} - 10 x - 2),

then

x

equals-

MEDIUM

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

Let

n

be a positive integer such that

\log_{2} \log_{2} \log_{2} \log_{2} \log_{2} (n) < 0 < \log_{2} \log_{2} \log_{2} \log_{2} (n)

. Let

l

be the number of digits in the binary expansion of

n

. Then the minimum and the maximum possible values of

l

are

HARD

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

If $3^{x} = 4^{x - 1}$ , then $x =$

EASY

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

\log_{4} x + \log_{16} x + \log_{64} x + \log_{256} x = \frac{25}{6}

then the value of

x

HARD

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

Students

A, B

and

C

measure the length of a room using

25 m

long measuring tape of least count

LC

0.5 cm,

meter-scale of

LC 0.1 cm

and a foot-scale of

LC 0.05 cm,

respectively. If the specified length of the room is

9.5 m,

then which of the following students will report the lowest relative error in the measured length?

(1 foot = 30.48 cm)

EASY

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

\log_{8} x + \log_{4} x + \log_{2} x = 11, x =

EASY

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

Among the following, the correct statement is :

MEDIUM

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

The value of

{({(\log_{2} 9)}^{2})}^{\frac{1}{\log_{2} (\log_{2} 9)}} \times {(\sqrt{7})}^{\frac{1}{\log_{4} 7}}

EASY

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

S = \frac{1}{2} (\frac{1}{2} + \frac{1}{3}) - \frac{1}{4} (\frac{1}{2^{2}} + \frac{1}{3^{2}}) + \frac{1}{6} (\frac{1}{2^{3}} + \frac{1}{3^{3}}) \dots \dots \dots

then

S =

MEDIUM

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

x + \log_{10} (1 + 2^{x}) = x \log_{10} 5 + \log_{10} 6,

then the value of

x

EASY

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

For

0 < m < 1

, which one of the following is correct?

HARD

Mathematics>Algebra>Logarithm and its Applications>Basics of Logarithm

Let

S

be the sum of the digits of the number

15^{2} \times 5^{18}

in base

10

. Then,

The number of zeros coming immediately after the decimal point in the value of 0.225 is/are (given log102 = 0.30103 )

Important Questions on Logarithm and its Applications

Learn and Prepare for any exam you want !

The number of zeros coming immediately after the decimal point in the value of ${(0 .2)}^{25}$ is/are (given $\log_{10} 2 = 0.30103$ )