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Solve: (1/2)^(log)(10)a^2+2>3/(2^((log)(...

Solve: `(1/2)^(log)_(10)a^2+2>3/(2^((log)_(10)(-a)))`

Text Solution

Verified by Experts

`(1/2)^(log_(10)a^(2))+2 gt 3/(2^(log_(10)(-a))) `
For this to be true, we must have `a lt 0`
` rArr 1/(2^(2 log(-a)))+2 gt 3/(2^(log (-a)))`
Putting ` y = 1/(2^(log(-a)))`, we get
`y^(2)+2 gt 3y`
` rArr y^(2) - 3y + 2 gt 0`
` rArr (y-1)(y-2) gt 0`
` rArr y lt 1 or y gt 2`
` rArr 2^(-log (-a)) lt 1 or 2^(-log(-a)) gt 2`
` rArr - log_(10)(-a) lt 0 or - log_(10)(-a) gt 1`
` rArr log_(10)(-a) gt 0 or log_(10)(-a) lt - 1`
` rArr -a gt 1 or -a lt 10^(-1)`
` rArr a lt - 1 or a gt - 0.1 `
` rArr a in (- infty, - 1) cup (-0.1, 0 ) `
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