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Exercise

ln⁡ ((sec⁡ (x)+tan⁡ (x))cos⁡ (x))\ln\:\left(\left(\sec\:\left(x\right)+\tan\:\left(x\right)\right)^{\cos\:\left(x\right)}\right)

Step-by-step Solution

1

Using the power rule of logarithms: log⁡a(xn)=n⋅log⁡a(x)\log_a(x^n)=n\cdot\log_a(x)

cos⁡(x)ln⁡(sec⁡(x)+tan⁡(x))\cos\left(x\right)\ln\left(\sec\left(x\right)+\tan\left(x\right)\right)

Final answer to the exercise

cos⁡(x)ln⁡(sec⁡(x)+tan⁡(x))\cos\left(x\right)\ln\left(\sec\left(x\right)+\tan\left(x\right)\right)

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ln ((sec (x)+tan (x))cos (x))
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