If x -log 51000 and y -log 72058 thenA- x-yB- x-yC- x-yD- None of these

The correct option is A x gt; y 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 gt; ...

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Byju's Answer

Standard IX

Mathematics

Logarithmic Inequality

If x =log 510...

Question

If $x = l o g_{5} (1000)$ and $y = l o g_{7} (2058)$ then

x > y

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x < y

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x = y

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None of these

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Solution

The correct option is A x > y
$x = l o g_{5} 1000 = 3 l o g_{5} 10 = 3 + 3 l o g_{5} 2 = 3 + l o g_{5} 8 y = l o g_{7} 2058 = l o g_{7} (7^{3} . 6) = 3 + l o g_{7} 6 A s l o g_{5} 8 > l o g_{5} 5 i . e ., l o g_{5} 8 > 1. ∴ x > 4 A n d l o g_{7} 6 < l o g_{7} 7 i . e ., l o g_{7} 6 < 1 ∴ y < 4; ∴ x > y .$

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If x=log5(1000) and y=log7(2058) then

The correct option is A x > y x=log51000=3 log510=3+3 log52=3+log58y=log72058=log7(73.6)=3+log76As log58>log55 i.e.,log58>1.∴x>4And log76<log77 i.e.,log76<1∴y<4;∴x>y.

If $x = l o g_{5} (1000)$ and $y = l o g_{7} (2058)$ then