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Question
Write the following expression as sum or difference of logarithm
In `[(root(3)(x - 2)(2x + 1)^4)/((x + 4)sqrt(2x + 4))]^2`
Solution
In `[(root(3)(x - 2)(2x + 1)^4)/((x + 4)sqrt(2x + 4))]^2`
= `2"In"[(root(3)(x - 2)(2x + 1)^4)/((x + 4)sqrt(2x + 4))]`
= `2{"In" [root(3)(x - 2)(2x + 1)^4] - "In"[(x + 4)sqrt(2x + 4)]}`
= `2{"In"(x - 2)^(1/3) + "In" (2x + 1)^4 - ["In"(x + 4) + "In"(2x + 4)^(1/2)]}`
= `2{1/3 "In"(x - 2) + 4"In"(2x + 1) - "In"(x + 4) - 1/2"In"(2x + 4)}`
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