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If log(5) x = a and log(2) y = a ," fin...

If ` log_(5) x = a and log_(2) y = a ," find "100^(2a-1)` in terms of x and y .

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The correct Answer is:
`((xy)^(4))/100`
` log_(5) x = a`
` :. x = 5^(a)`
` log_(2) y = a`
` :. y = 2^(a)`
` 100^(2a-1)=(5^(2)2^(2))^(2a) xx 100^(-1)`
` = (5^(a)2^(a))^(4) xx 100^(-1)`
` = ((xy)^(4))/100`
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