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Number of integral values of $x$ the inequality $\log_{10} (\frac{2 x - 2007}{x + 1}) \leq 0$ holds true, is

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Important Questions on Logarithms

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Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

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

MEDIUM

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

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>Logarithms>Logarithmic Equations and Inequalities

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

then

y =

HARD

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

Let

S

be the sum of the digits of the number

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

in base

10

. Then,

MEDIUM

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

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

then the value of

x

EASY

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

For

0 < m < 1

, which one of the following is correct?

EASY

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

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

MEDIUM

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

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}

EASY

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

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

then

x =

HARD

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

The solution set of the inequality

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

HARD

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

\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>Logarithms>Logarithmic Equations and Inequalities

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

MEDIUM

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

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}

MEDIUM

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

Number of real values of

x

which satisfy

l o g_{2} x^{2} + \log_{2} (x + 2) = 4

is/are

MEDIUM

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

Set of all the values of

x

satisfying the inequality

\log_{x + \frac{1}{x}} (\log_{2} \frac{x - 1}{x + 2}) > 0

EASY

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

Solve

\log_{3} (5 x - 1) > 0

EASY

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

Which of the following is negative ?

MEDIUM

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

\frac{1}{\log_{3} π} + \frac{1}{\log_{4} π} > x

, then

x

EASY

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

The number of solution of

\log_{\sin x} 2^{\tan x} > 0

in the interval

(0, \frac{π}{2})

HARD

Mathematics>Algebra>Logarithms>Logarithmic Equations and Inequalities

\log_{\frac{1}{3}} (x^{2} + 2 x) > 0

, if

x

belongs to the set

Number of integral values of x the inequality log102x-2007x+1≤0 holds true, is

Important Questions on Logarithms

Learn and Prepare for any exam you want !

Number of integral values of $x$ the inequality $\log_{10} (\frac{2 x - 2007}{x + 1}) \leq 0$ holds true, is