SOLUTION: Prove that log 3=(log 2)+ (1/2)-(1/8)+(1/24)-(1/64)+....and so on.
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Question 464432: Prove that log 3=(log 2)+ (1/2)-(1/8)+(1/24)-(1/64)+....and so on.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
This is true if and only if
,
because it will satisfy the logarithm identity  = \log(a) + \log(b))
. However, the above series is equal to ln 3/2. If you know the Taylor series for ln x centered at 1
 - \frac{1}{2}(x-1)^2 + \frac{1}{3}(x-1)^3...)
We can replace x = 3/2 and get a true result. Hence the original equation is true.
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