Question

log [tex] \sqrt{2} [\tex] 64

Answer 1

Answer:

12

Step-by-step explanation:

Let say answer = x

then

$(\sqrt{2})^x = 64$

$2^{(x/2)} = 64$

$2^{6} = 64$

$\frac{x}{2} = 6$

x = 2 × 6

x = 12

Answer 2

Step-by-step explanation:

$( { \sqrt{2} })^{x} = 64 \\ \\ {(2)}^{ \frac{x}{2} } = 64..............(1) \\ (this \: is \: because \: \sqrt{2} = {2}^{ \frac{1}{2} } ) \\ but \: we \: already \: know \: that = > \\ {2}^{6} = 64....................(2) \\ \\ from \: (1) \: and \: (2) \: we \: can \: conclude. \\ \frac{x}{2} = 6 \\ x = 6 \times 2 \\ ............(multiplying \: both \: sides \: by \: 2) \\ \\ x = 12.. \\ \\ \\ hope \: it \: helps \: you \: dear....$