The domain of the function f ( x ) = log 3 x 2 - 4 x + 7 is

set of real numbers - { 3 , 2 , 7 } .

set of non-negative real numbers.

HARD

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If $\log_{6} 15 = α$ and $\log_{12} 18 = β$ , then the value of $\log_{25} 24 =$

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Important Questions on Relations and Functions

MEDIUM

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

The value of

\log_{2} 32 =

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

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

, the value of

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

MEDIUM

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

The solution of

\log_{\sqrt{3}} x + \log_{\sqrt[4]{3}} x + \log_{\sqrt[6]{3}} x + \dots . . + \log_{\sqrt[16]{3}} x = 36

, find

x

EASY

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

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

and

c = \log_{7} 2

, then

\log_{140} 63

in terms of

a, b, c

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

HARD

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

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} =

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}}

MEDIUM

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

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

then the values of

x

are

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

EASY

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

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

, then find the value of

y

in term of

x

MEDIUM

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

\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 :

EASY

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

\log_{a} (\sqrt{3}) = \frac{1}{6}

find the value of '

a

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

\log 9 + \log 5

is expressed as ...............

EASY

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

For which of the following values of

' x',

does the function

f (x) = \log [\{\sqrt{(25 - x^{2})}\} / (2 - x)]

have the real values?

MEDIUM

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

The domain of the function

f (x) = \log (3 x^{2} - 4 x + 7)

EASY

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

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

, then

x

is equal to

MEDIUM

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

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

, then

x

is:

EASY

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

The logarithm of

\frac{1}{256}

to the base

2 \sqrt{2}

If log6⁡15= α and log12⁡18= β , then the value of log25⁡24=

Important Questions on Relations and Functions

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If $\log_{6} 15 = α$ and $\log_{12} 18 = β$ , then the value of $\log_{25} 24 =$