Given that \({{\log }_{2}}\left[ {{\log }_{3}}\left( {{\log }_{5}}x \right) \right]={{\log }_{3}}\le

Question

Given that ${{\log }_{2}}\left[ {{\log }_{3}}\left( {{\log }_{5}}x \right) \right]={{\log }_{3}}\left[ {{\log }_{5}}\left( {{\log }_{2}}y \right) \right]={{\log }_{5}}\left[ {{\log }_{2}}\left( {{\log }_{3}}z \right) \right]=0$, express $x-y-z$ as a product of its prime factors.

Accepted Answer

$2^2\times3\times7$.

Exponential and Logarithmic Functions - Solving Logarithm Equations

Exponential and Logarithmic Functions - Solving Logarithm Equations

Solution:

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