Question

Logarithms equation: log√2x=12

Answer 1

`\large\boxed{x=64}`

Explanation:

`\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}\ (√(a))^2=a\\\\x=2^6\\\\x=64`