If-y-a-1-1-log-a-x-and-z-a-1-1-log-a-y-show-that-x-a-1-1-log-a-z-

Question Number 42549 by Tawa1 last updated on 27/Aug/18

If y = a^{\frac{1}{1 - \log_{a} x}} and z = a^{\frac{1}{1 - \log_{a} y}} . show that x = a^{\frac{1}{1 - \log_{a} z}}

Answered by math1967 last updated on 27/Aug/18

{l o g}_{a} y = \frac{1}{1 - {l o g}_{a} x} \Rightarrow {l o g}_{a} x = 1 - \frac{1}{{l o g}_{a} y}

s i m i l a r l y {l o g}_{a} y = 1 - \frac{1}{{l o g}_{a} z}

∴ {l o g}_{a} x = 1 - \frac{1}{1 - \frac{1}{{l o g}_{a} z}} = \frac{- 1}{{l o g}_{a} z - 1} = \frac{1}{1 - {l o g}_{a} z}

∴ x = a^{\frac{1}{1 - {l o g}_{a} z}}

Commented by Tawa1 last updated on 27/Aug/18

God bless you sir

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