Let for . Which of the following expressions is equivalent to…

MATHEMATICS · Single correct · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

Let y=x2(3x−1)51+x4y = x^{2}(3x-1)^{5}\sqrt{1+x^{4}} for x>0x>0. Which of the following expressions is equivalent to ln⁡y\ln y? (a) 2ln⁡x+5ln⁡(3x−1)+ln⁡(1+x4)2\ln x + 5\ln(3x-1) + \ln(1+x^{4}) (b) ln⁡x+5ln⁡(3x−1)+12ln⁡(1+x4)\ln x + 5\ln(3x-1) + \dfrac{1}{2}\ln(1+x^{4}) (c) 2ln⁡x+5ln⁡(3x−1)+12ln⁡(1+x4)2\ln x + 5\ln(3x-1) + \dfrac{1}{2}\ln(1+x^{4}) (d) 2ln⁡x+15ln⁡(3x−1)+12ln⁡(1+x4)2\ln x + \dfrac{1}{5}\ln(3x-1) + \dfrac{1}{2}\ln(1+x^{4})

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