Question

Logarithm question

Simplify 1/ log_{​​​​xy}(xyz)+ 1/log_{​​​​yz}(xyz)+1/ log_{​​​​zx}(xyz)

Answer 1

Formula

log m to the base n =logm/logn.

= 1/(logxyz/log xy) + 1/(log xyz/log yz) + 1/(log xyz/log zx).

=log xy/log xyz +log yz/log xyz +log zx/log xyz.

=(1/log xyz). (logxy+logyz+log zx).

=(1/log xyz).(logxy.yz.zx).

=log(xyz)^2/logxyz.

= 2.logx.y.z/logx.y.z

= 2 , Answer.