Answer:
[tex]\large\boxed{x=64}[/tex]
Step-by-step explanation:
[tex]\log_ab=c\iff a^c=b\\===================\\\\Domain:\ x>0\\\\\log_{\sqrt2}x=12\iff x=(\sqrt2)^{12}\\\\\text{use}\ (a^n)^m=a^{nm}\\\\x=(\sqrt2)^{2\cdot6}\\\\x=\bigg[(\sqrt2)^2\bigg]^6\\\\\text{use}\ (\sqrt{a})^2=a\\\\x=2^6\\\\x=64[/tex]
