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Q.

In which of the following ,m>n(m,n∈R) ?

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a

m=log2⁡52 and n=log2⁡20

b

m=log10⁡2 and n=log10⁡103

c

m=log10⁡5⋅log10⁡20 and n=1

d

m=log1/2⁡13 and n=log1/3⁡12

answer is A.

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Detailed Solution

1  m−n=log2⁡52−log2⁡5+2=log2⁡5−2log2⁡5+1>0∴ m>n2 23<10 or  2<101/3 or  log10⁡21∴ m>n( as n>0)
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