21The value of log 2log 3- - log 1001009998

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Fundamental Laws of Logarithms

21The value o...

Question

The value of $l o g_{2} l o g_{3} . . . . l o g_{100}^{100^{99^{98^{⋮^{2^{1}}}}}}$

0.0

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Solution

The correct option is B 1
$l o g_{2} . l o g_{3} . . . . l o g_{99} l o g_{100} 100^{99^{98^{⋮^{2^{1}}}}} = l o g_{2} l o g_{3} . . . . l o g_{99} 99^{98^{⋮^{2^{1}}}} [l o g_{100} 100 = 1] S i m i l a r l y, l o g_{2} l o g_{3} . . . . l o g_{98} 98^{97^{⋮^{2^{1}}}} = l o g_{2} l o g_{3} . . . . l o g_{97} 97^{96^{⋮^{2^{1}}}} = l o g_{2} l o g_{3} 3^{2^{1}} = l o g_{2} 2^{1} l o g_{3} 3 = l o g_{2} 2 = 1.$

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Similar questions

Q. The value of

l o g_{2} l o g_{3} . . . . l o g_{100}^{100^{99^{98^{⋮^{2^{1}}}}}}

x^{2} - p x + log 2 log 3 = 0

has one root as

log 2

. Find the value of

p

Q. Fill in the Blanks
Question 21
The Y-coordinate of the point (2,4) is ___.

Question 21
The reciprocal of $\frac{- 3}{8} \times (\frac{- 7}{13})$ is
(a) $\frac{104}{21}$
(b) $\frac{- 104}{21}$
(c) $\frac{21}{104}$
(d) $\frac{- 21}{104}$

Question 21
The median of the data 78, 56, 22, 34, 45, 54, 39, 68, 54 and 84 is:

A) 45
B) 49.5
C) 54
D) 56

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The value of log2 log3 ....log1009998⋮21100

The correct option is B 1log2.log3....log99log100 1009998⋮21=log2log3....log99 9998⋮21 [log100100=1]Similarly,log2log3....log989897⋮21=log2log3....log979796⋮21=log2log3321=log2 21log3 3=log2 2=1.

The value of $l o g_{2} l o g_{3} . . . . l o g_{100}^{100^{99^{98^{⋮^{2^{1}}}}}}$