Question

If xlog 2 = ylog 4=z log8, then

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Answer 1

Answer:

is attached i Hope this helps you

Answer 2

The correct option is choice (c).

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Given: $x\log2=y\log4=z\log8$

$\implies x\log2=y\log2^2=z\log2^3$

$\implies x\log2=2y\log2=3z\log2$

$\implies y=\dfrac{x}{2} ,z=\dfrac{x}{3}$

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Choice (a)

LHS = $x$

RHS = $6(y+z)=6(\dfrac{x}{2} +\dfrac{x}{3} )=6\times \dfrac{5x}{6} =\boxed{5x}$

Hence, LHS ≠ RHS.

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Choice (b)

LHS = $6x$

RHS = $y+z=\dfrac{x}{2} +\dfrac{x}{3} =\boxed{\dfrac{5x}{6} }$

Hence, LHS ≠ RHS.

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Choice (c)

LHS = $5x$

RHS = $6(y+z)=6(\dfrac{x}{2} +\dfrac{x}{3} )=6\times \dfrac{5x}{6} =\boxed{5x}$

Hence, LHS = RHS.

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Choice (d)

LHS = $5(x+y)=5(x+\dfrac{x}{2} )=\boxed{\dfrac{15x}{2} }$

RHS = $6z=6\times \dfrac{x}{3} =\boxed{2x}$

Hence, LHS ≠ RHS.