Given that log 2=a and log 3=b, write log √96 in terms of a and b
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Answer:
log √96 = ½(5a + b)
Step-by-step explanation:
we know that,
log 2 = a
log 3 = b
now,
log √96 = ½ log 96
= ½ [log (16 x 3 x 2)]
= ½ [log 16 + log 3 + log 2]
= ½ [log 2⁴ + log 3 + log 2]
= ½ [4 x log 2 + log 3 + log 2]
= ½ [5 x log 2 + log 3]
= ½ [5a + b]
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