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Question

The value of the determinant
∣ ∣ ∣ ∣ ∣loga(xy)loga(yz)loga(zx)logb(yz)logb(zx)logb(xy)logc(zx)logc(xy)logc(yz)∣ ∣ ∣ ∣ ∣ is


A

loga (xyz)+logb (xyz)+logc (xyz)

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B

a loge x+b loge y+c loge z

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C

-1

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D

None of these

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Solution

The correct option is D

None of these


logn m=ln mln nΔ=∣ ∣ ∣ ∣ ∣loga(xy)loga(yz)loga(zx)logb(yz)logb(zx)logb(xy)logc(zx)logc(xy)logc(yz)∣ ∣ ∣ ∣ ∣
Δ=1ln a. ln b. ln c∣ ∣ ∣ ∣ ∣ln(xy)ln(yz)ln(zx)ln(yz)ln(zx)ln(xy)ln(zx)ln(xy)ln(yz)∣ ∣ ∣ ∣ ∣
ln mn=ln mln n
Δ=1ln a. ln b. ln c∣ ∣ ∣(ln xln y)(ln yln z)(ln zln x)(ln yln z)(ln zln x)(ln xln y)(ln zln x)(ln xln y)(ln yln z)∣ ∣ ∣
Δ=1ln a. ln b. ln c∣ ∣ ∣000(ln yln z)(ln zln x)(ln xln y)(ln zln x)(ln xln y)(ln yln z)∣ ∣ ∣=0(R1R1+R2+R3)


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