Basic of Logarithms
hard

જો $x = {\log _5}(1000)$ અને $y = {\log _7}(2058)$ તો

A

$x > y$

B

$x < y$

C

$x = y$

D

એકપણ નહી.

Solution

(a) $x = {\log _5}1000 = 3{\log _5}10 = 3 + 3{\log _5}2 = 3 + {\log _5}8$

$y = {\log _7}2058 = {\log _7}({7^3}.6) = 3 + {\log _7}6$

As ${\log _5}8 > {\log _5}5$ i.e., ${\log _5}8 > 1$. $x > 4$

And ${\log _7}6 < {\log _7}7$ i.e., ${\log _7}6 < 1$

$\therefore y < 4$;

$\therefore x > y$.

Standard 11
Mathematics

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