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Solve (log)(2x)2+(log)4 2x=-3//2....

Solve `(log)_(2x)2+(log)_4 2x=-3//2.`

Text Solution

Verified by Experts

Given equation is
` 1/(1+log_(2)x)+(log_(2)2x)/2 =- 3/2`
` or 1/(1+log_(2) x)+(1+log_(2)x)/2 =- 3/2`
Let ` 1+ log_(2) x = y`
` rArr 1/y + y/2 =- 3/2`
` or 2+y^(2)+3y = 0`
` or y =- 1 or -2`
` rArr 1+ log_(2)x =- 1 or -2`
`or log_(2)x =- 2 or -3`
` rArr x = 2^(-2) or 2^(-3)`
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CENGAGE PUBLICATION-LOGARITHM AND ITS PROPERTIES-Example 1.9
  1. Solve (log)(2x)2+(log)4 2x=-3//2.

    Text Solution

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