Solve for x and y:
x= $l o g_{5} 2 + l o g_{5} 9 + l o g_{5} 3$
y= $l o g_{2} 18 - l o g_{2} 3 + l o g_{2} 4$

x =

l o g_{5} 54

and y =

l o g_{5} 24

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x =

l o g_{5} 54

and y =

l o g_{2} 24

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x =

l o g_{5} 64

and y =

l o g_{5} 24

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x =

l o g_{5} 54

and y =

l o g_{5} 25

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Solution

The correct option is B x = $l o g_{5} 54$ and y = $l o g_{2} 24$
x = $l o g_{5} 2 + l o g_{5} 9 + l o g_{5} 3$
$= l o g_{5} (2 \times 9 \times 3) [∴ l o g_{a} b + l o g_{a} c = l o g_{a} (b \times c)]$

$= l o g_{5} 54$

b) $l o g_{2} 18 - l o g_{2} 3 + l o g_{2} 4$
$= l o g_{2} (18 \times 4) - l o g_{2} 3 [∴ l o g_{a} b + l o g_{a} c = l o g_{a} (b \times c)]$
$= l o g_{2} 72 - l o g_{2} 3$
$= l o g_{2} (\frac{72}{3}) [∴ l o g_{a} b - l o g_{a} c = l o g_{a} (\frac{b}{c})]$
$= l o g_{2} 24$
So, option b is correct.

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