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Solve (log)(0. 04)(x-1)geq(log)(0. 2)(x-...

Solve `(log)_(0. 04)(x-1)geq(log)_(0. 2)(x-1)`

Text Solution

Verified by Experts

` log_(0.04) (x-1) ge log_(0.2)(x-1)`
` or log_((0.2^(2)))(x-1) ge log_(0.2)(x-1)`
` or 1/2 log_(0.2)(x-1) ge log_(0.2) (x-1)`
` or log_(0.2)(x-1) ge 2 log_(0.2)(x-1)`
` or log_(0.2)(x-1) ge log_(0.2)(x-1)^(2)`
` or (x-1) le (x-1)^(2)`
` or (x-1)^(2)-(x-1) ge 0`
` or (x-1)(x-1-1) ge 0`
`or (x-1)(x-2) ge 0`
` or x le 1 or x ge 2`
`"Also," x gt 1,`
`" Hence, "x ge 2.`
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Knowledge Check

  • If log_(0.2) (x-1) gt log_(0.04) (x+5) then

    A
    `-1 lt x lt 4`
    B
    `2 lt x lt 3`
    C
    `1 lt x lt 4`
    D
    `1lt x lt 3`
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