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Mathematics
Emily Lee
5 March, 03:13
Prove that 1:loga ab + 1:logb ab=1
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Nyla Craig
5 March, 03:22
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See below.
Step-by-step explanation:
1 : loga ab + 1 : logb ab
= 1 / (loga ab) + 1 / (loga ab / loga b) { change of log base)
= 1 / (loga ab) + loga b / (loga ab)
= (1 + loga b) / loga ab
= (1 + loga b) / (loga a + loga b) Now loga a = 1 so we have:
((1 + loga b) / (1 + loga b)
= 1.
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