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

The correct option is B x gt;yx=log_5(1000) =log_5(5^3.8)=3+log_5 8 gt;3+1=4 y=log_7 (2058)=log_7(7^3.6)=3+log_7 6 gt;3+1=4 since x gt;4 and y lt;4 ...

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Byju's Answer

Standard XII

Mathematics

Logarithmic Inequalities

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

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Solution

The correct option is A x>y
$x = l o g_{5} (1000) = l o g_{5} (5^{3} .8) = 3 + l o g_{5} 8 > 3 + 1 = 4$
$y = l o g_{7} (2058) = l o g_{7} (7^{3} .6) = 3 + l o g_{7} 6 > 3 + 1 = 4$
since $x > 4$ and $y < 4$ $∴ x > y$

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

The correct option is A x>yx=log5(1000)=log5(53.8)=3+log5 8>3+1=4 y=log7(2058)=log7(73.6)=3+log7 6>3+1=4 since x>4 and y<4 ∴ x>y

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

The correct option is A x>y
$x = l o g_{5} (1000) = l o g_{5} (5^{3} .8) = 3 + l o g_{5} 8 > 3 + 1 = 4$
$y = l o g_{7} (2058) = l o g_{7} (7^{3} .6) = 3 + l o g_{7} 6 > 3 + 1 = 4$
since $x > 4$ and $y < 4$ $∴ x > y$