If x = _5 (1000) and y = _7 (2058) then - Vidyadip

MCQ

If $x = {\log _5}(1000)$ and $y = {\log _7}(2058)$ then

✓
$x > y$
B
$x < y$
C
$x = y$
D
None of these

✓

Answer

Correct option: A.

$x > y$

a
(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., ${\log _7}6 < 1$

$\therefore y < 4$;

$\therefore x > y$.

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