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Let $a, b, c, d$ are positive integers such that $\log_{a} b = \frac{3}{2} & \log_{c} d = \frac{5}{4} .$ If $(a - c) = 9,$ then the value of $(b - d)$ is

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Important Questions on Logarithm and its Applications

HARD

Mathematics>Algebra>Logarithm and its Applications>Logarithmic Equations and Inequalities

Let

f

be a function defined on the set of all positive integers such that

f (x y) = f (x) + f (y)

for all positive integers

x, y .

f (12) = 24

and

f (8) = 15

, the value of

f (48)

MEDIUM

Mathematics>Algebra>Logarithm and its Applications>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>Logarithm and its Applications>Logarithmic Equations and Inequalities

The value of

{(\log_{3} 30)}^{- 1} + {(\log_{4} 900)}^{- 1} + {(\log_{5} 30)}^{- 1}

MEDIUM

Mathematics>Algebra>Logarithm and its Applications>Logarithmic Equations and Inequalities

\log_{5} \log_{8} (x^{2} - 1) = 0

, then a possible value of

x

MEDIUM

Mathematics>Algebra>Logarithm and its Applications>Logarithmic Equations and Inequalities

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

then the value of

x

MEDIUM

Mathematics>Algebra>Logarithm and its Applications>Logarithmic Equations and Inequalities

The inequality

\log_{2} \frac{3 x - 1}{2 - x} < 1

holds true for

EASY

Mathematics>Algebra>Logarithm and its Applications>Logarithmic Equations and Inequalities

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

then

y =

EASY

Mathematics>Algebra>Logarithm and its Applications>Logarithmic Equations and Inequalities

\log_{10} x + \log_{10} x^{2} = 2 \log_{10} x + 1

, then what is the value of

x

EASY

Mathematics>Algebra>Logarithm and its Applications>Logarithmic Equations and Inequalities

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

then

x =

HARD

Mathematics>Algebra>Logarithm and its Applications>Logarithmic Equations and Inequalities

The solution set of the inequality

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

HARD

Mathematics>Algebra>Logarithm and its Applications>Logarithmic Equations and Inequalities

The value of

0 . 04^{\log_{\sqrt{5}} (\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \dots)}

HARD

Mathematics>Algebra>Logarithm and its Applications>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>Logarithm and its Applications>Logarithmic Equations and Inequalities

What is the solution of the equation

x \log_{10} (\frac{10}{3}) + \log_{10} 3 = \log_{10} (2 + 3^{x}) + x

MEDIUM

Mathematics>Algebra>Logarithm and its Applications>Logarithmic Equations and Inequalities

The inequality

\log_{a} {f (x)} < \log_{a} {g (x)}

implies that

EASY

Mathematics>Algebra>Logarithm and its Applications>Logarithmic Equations and Inequalities

5^{x - 1} = {(2.5)}^{{\log_{10}}^{5}}

, then what is the value of

x

EASY

Mathematics>Algebra>Logarithm and its Applications>Logarithmic Equations and Inequalities

\log x = 1.2500 and y = x^{\log x}

, then what is logy equal to?

EASY

Mathematics>Algebra>Logarithm and its Applications>Logarithmic Equations and Inequalities

What is

\log_{10} 31.25

equal to?

MEDIUM

Mathematics>Algebra>Logarithm and its Applications>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}

MEDIUM

Mathematics>Algebra>Logarithm and its Applications>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>Logarithm and its Applications>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}

Let a,b,c,d are positive integers such that logab=32 & logcd=54. If a-c=9, then the value of b-d is

Important Questions on Logarithm and its Applications

Learn and Prepare for any exam you want !

Let $a, b, c, d$ are positive integers such that $\log_{a} b = \frac{3}{2} & \log_{c} d = \frac{5}{4} .$ If $(a - c) = 9,$ then the value of $(b - d)$ is