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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Given that log 2 = a and log 3 = b, write log96 in terms of a and b - Mathematics and Statistics

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प्रश्न

Given that log 2 = a and log 3 = b, write `log sqrt(96)` in terms of a and b

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उत्तर

log 2 = a and log 3 = b

`log sqrt(96) = 1/2 log (96)`

= `1/2 log (2^5 xx 3)`

= `1/2(log 2^5 + log 3)`  ...[log mn = log m + log n]

= `1/2 (5log 2 + log 3)`  ..[log mn = nlog m]

= `(5"a" + "b")/2`

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पाठ 6: Functions - Exercise 6.1 [पृष्ठ ११९]
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