Answer
(a) $\ln(e^{\sec\theta})=\sec\theta$
(b) $\ln e^{e^x}=e^x$
(c) $\ln (e^{2\ln x})=2\ln x$
Work Step by Step
This whole exercise is based on this property: $$\ln e^x=x\hspace{1cm}x\gt0$$
(a) $$\ln(e^{\sec\theta})=\ln e^{\sec\theta}=\sec\theta$$
Therefore, $$\ln(e^{\sec\theta})=\sec\theta$$
(b) $$\ln e^{e^x}=\ln e^{(e^x)}=e^x$$
Therefore, $$\ln e^{e^x}=e^x$$
(c) $$\ln (e^{2\ln x})=\ln e^{2\ln x}=2\ln x$$
Therefore, $$\ln (e^{2\ln x})=2\ln x$$
