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If y = a^(1/(1-log(a) x)) and z = a^(1/...

If ` y = a^(1/(1-log_(a) x)) and z = a^(1/(1-log_(a)y))",then prove that "x=a^(1/(1-log_(a)z))`

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` log_(a) y = 1/(1 - log_(a) x)`
` rArr 1 - log_(a) y = 1 - 1/(1-log_(a) x)`
` = (-log_(a) x)/(1-log_(a)x)`
` or 1/(1-log_(a)y)=(1-log_(a)x)/(-log_(a) x)` ...(i)
` "But " z = a^(1/(1-log_(a)y))`
` rArr log_(a) z =1/(1=log_(a)y)=-1/(log_(a) x) +1`
` or 1/(log_(a)x) =1-log_(a)z`
` or log_(a) x = 1/(1-log_(a)z)`
` or x = a^(1/(1-log_(a)z)`
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