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If sum log(2)x+log(4) x + log(16) x + l...

If sum ` log_(2)x+log_(4) x + log_(16) x + log_(256) x + …=6,` then find the value of x.

Text Solution

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`log_(2)x+log_(4)x+log_(16)x+log_(32)x+ * * * = 6`
` rArr log_(2) x+ log_(2^(2))x+log_(2^(4))x+log_(2^(5))x+ * * * = 6`
`rArr (1+1/2+1/4+1/8+...)log_(2) x= 6`
` rArr 1/(1-1/2)log_(2) x = 6`
` rArr log_(2) x = 3`
` rArr x = 8`
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