4log8sqrt2

If it is base 8 it should have been wrtitten like this

4log_8(sqrt2)

or

4 times the log of sqrt2 base 8

or

$$\\Let\\\\
x=4log_8\sqrt{2}\\\\
x=log_8\sqrt{2}^4\\\\
x=log_8 2^2\\\\
x=log_8 4\\\\
4=8^x\\\\
2^2=2^{3x}\\\\
2=3x\\\\
x=\frac{2}{3}\\\\
4log_8\sqrt{2}=\frac{2}{3}$$

Is this base 10 or basse 2?

Alsao I could do with some brackets because I do not known what you are taking the log of  :/

This is base 8

$${\mathtt{4}}{\mathtt{\,\times\,}}{log8}{\left({\sqrt{{\mathtt{2}}}}\right)} = {\mathtt{4}}{\mathtt{\,\times\,}}{{log}}_{{\mathtt{8}}}{\left({\mathtt{1.414\: \!213\: \!562\: \!373\: \!095}}\right)}$$

And is this what you mean?

angelo