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$\log (\cosh 3+\sinh 3)+\log (\cosh 3-\sinh 3)=$
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$\log (\cosh 3+\sin h 3)+\log (\cosh 3-\sinh 3)$
$\begin{aligned} & =\log \left(\frac{\mathrm{e}^3+\mathrm{e}^{-3}}{2}+\frac{\mathrm{e}^3 \mathrm{e}^{-3}}{2}\right)+\log \left(\frac{\mathrm{e}^3+\mathrm{e}^{-3}}{2}-\frac{\mathrm{e}^3-\mathrm{e}^{-3}}{2}\right) \\ & =\log \left(\mathrm{e}^3\right)+\log \left(\mathrm{e}^{-3}\right) \\ & =3-3=0\end{aligned}$
$\begin{aligned} & =\log \left(\frac{\mathrm{e}^3+\mathrm{e}^{-3}}{2}+\frac{\mathrm{e}^3 \mathrm{e}^{-3}}{2}\right)+\log \left(\frac{\mathrm{e}^3+\mathrm{e}^{-3}}{2}-\frac{\mathrm{e}^3-\mathrm{e}^{-3}}{2}\right) \\ & =\log \left(\mathrm{e}^3\right)+\log \left(\mathrm{e}^{-3}\right) \\ & =3-3=0\end{aligned}$
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