If logₐb + logₓc + logca vanishes where a, b and c are positive reals different than unity then

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Basic of Logarithms

normal

If $log_ab + log_bc + log_ca$ vanishes where $a, b$ and $c$ are positive reals different than unity then the value of $(log_ab)^3 + (log_bc)^3 + (log_ca)^3$ is

A

an odd prime

B

an even prime

C

an odd composite

D

an irrational number

Solution

$x + y + z = 0$

$\Rightarrow$ $x^3 + y^3 + z^3 = 3xyz$

$\Rightarrow 3$

Standard 11

Mathematics

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