Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

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Suppose $n$ be an integer greater than $1$ . Let $a_{n} = \frac{1}{\log_{n} 2002} .$ Suppose $b = a_{2} + a_{3} + a_{4} + a_{5}$ and $c = a_{10} + a_{11} + a_{12} + a_{13} + a_{14} .$ Then find the value of $(c - b)$

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Important Questions on Relations and Functions

EASY

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

If

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

, the value of

x (\frac{1}{y} + \frac{1}{z} + \frac{1}{w})

is

EASY

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

If

2^{x} {.3}^{x + 4} = 7^{x}

, then

x

is equal to

HARD

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

If

N = m!

(where

m

is a fixed positive integer

> 2

), then

\frac{1}{\log_{2} N} + \frac{1}{\log_{3} N} + \frac{1}{\log_{4} N} + ..... + \frac{1}{\log_{m} N} =

HARD

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

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

MEDIUM

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

If

3^{x + 1} = 6^{\log_{2} 3}

, then

x

is:

EASY

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

The common difference of A.P.

\log_{2} 2, \log_{2} 4, \log_{2} 8

is

MEDIUM

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

\log_{7} \log_{7} \sqrt{7 \sqrt{7 \sqrt{7}}}

is equal to

EASY

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

\log_{10} 0.001 =

_____

EASY

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

If

a = \log_{2} 3, b = \log_{2} 5

and

c = \log_{7} 2

, then

\log_{140} 63

in terms of

a, b, c

is

MEDIUM

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

If

\log_{2} 6 + \frac{1}{2 x} = \log_{2} (2^{\frac{1}{x}} + 8)

then the values of

x

are

EASY

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

If

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 =

EASY

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

The logarithm of

\frac{1}{256}

to the base

2 \sqrt{2}

is

EASY

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

Find the value of

\log_{5} \sqrt{625}

MEDIUM

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

The value of

\log_{2} 32 =

EASY

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

Expand log₁₀

385

EASY

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

If

x, y, z

are positive real numbers such that

x^{12} = y^{16} = z^{24}

, and the three quantities

3 \log_{y} x, 4 \log_{z} y, n \log_{x} z

are in arithmetic progression, then the value of

n

is

EASY

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

Show that,

\log (\frac{162}{343}) + 2 \log (\frac{7}{9}) - \log (\frac{1}{7}) = \log 2

MEDIUM

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

The solution of the equation

3^{\log_{a} x} + 3 x^{\log_{a} 3} = 2

is given by

MEDIUM

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

If

\log_{\sqrt{3}} x + \log_{\sqrt[3]{5}} x + \log_{\sqrt[4]{5}} x + . . . . . .

up to

7

terms

= 35

, then the value of

x

is :

MEDIUM

Mathematics>Algebra>Relations and Functions>Logarithmic Function and its Properties

The value of

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

is