For with , which of the following expressions correctly represents after taking…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

For y=(x2+1)xy=(x^{2}+1)^{\sqrt{x}} with x>0x>0, which of the following expressions correctly represents ln⁡y\ln y after taking natural logarithm on both sides? (a) ln⁡y=ln⁡(x2+1)x\ln y=\dfrac{\ln(x^{2}+1)}{\sqrt{x}} (b) ln⁡y=(x)ln⁡(x2+1)\ln y=(\sqrt{x})^{\ln(x^{2}+1)} (c) ln⁡y=x ln⁡(x2+1)\ln y=\sqrt{x}\,\ln(x^{2}+1) (d) ln⁡y=x ln⁡(x2+1)\ln y=x\,\ln(x^{2}+1)

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