Solutiile ecuatiei $(\sqrt{3}+1)^x+(\sqrt{3}-1)^x=4(\sqrt{2})^x$ sunt:
$
\begin{array}{l}
x \in\left\{\log _{\sqrt{3}+1}(2+\sqrt{5}), \log _{\sqrt{3}+1}(-2+\sqrt{5})\right\} \\
x \in\left\{\log _{\sqrt{3}+1}(2+\sqrt{5})\right\} \\
x \in\left\{\log _{\sqrt{2}}(1+\sqrt{3}), \log _{\sqrt{2}}(-1+\sqrt{3})\right\} \\
x \in\left\{\log _{2+\sqrt{3}}(1+\sqrt{3})\right\} \\
x \in\left\{\log _{\sqrt{3}+2}(7+4 \sqrt{3}), \log _{\sqrt{3}+2}(7-4 \sqrt{3})\right\} . \\
x \in\left\{\log _{\sqrt{5}+1}(2+\sqrt{5})\right\}
\end{array}
$