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If (log)(10)2=0. 30103 ,(log)(10)3=0. 47...

If `(log)_(10)2=0. 30103 ,(log)_(10)3=0. 47712 ,` then find the number of digits in `3^(12)x2^8dot`

Text Solution

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Let ` y = 3^(12) xx 2^(8)`
` rArr log_(10) y = 12 log_(10) 3+ 8log_(10) 2`
` = 12 xx 0.47712 + 8 xx 0.30103`
` = 5.72544+ 2.40824`
` = 8.13368`
` :. ` Number of digits in y = 8 + 1 = 9.
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