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If x^((1)/(12)) = 49^((1)/(24)) find th...

If `x^((1)/(12)) = 49^((1)/(24))` find the value of x. (ii) If `(125)^(x) =(25)/(5^(x))`, find x.

Text Solution

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We have .
(i) `x^((1)/(12)) = 49 ^((1)/( 24)) hArr ( x ^((1)/(12)))^( 12)) = ( 49 ^( (1)/( 24 )) )^( 12) `
` hArr x ^(( (1)/(12) xx 12 )) = 49 ^(( (1)/( 24) xx 12)) `
` hArr x = 49 ^((1)/(2)) = sqrt ( 49 ) = 7`.
(ii) ` ( 125)^(x) = ( 25)/( 5 ^(x)) hArr ( 5 ^(3)) ^(x) = ( 5 ^(2))/( 5 ^( x ) ) `
` hArr 5 ^( 3x ) = 5 ^( 2 - x ) `
`hArr 3x = 2 - x rArr 4 x = 2 rArr x = ( 2 )/(4) = (1)/(2) `.
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