To solve the equation log8(x) + log√2(x) = 14, we can first simplify it using logarithmic properties.

Since log8(x) + log√2(x) = log8(x) + 0.5*log2(x), we can combine the logarithms using the property loga(x) + loga(y) = loga(xy).

Therefore, log8(x) + 0.5log2(x) = log8(x √2) = 14.

Now, we can rewrite log8(x √2) = 14 as 8^14 = x √2.

Solving for x, we get x = 8^14 / √2.

Calculating 8^14 and √2, we get:

8^14 ≈ 2.2518 x 10^10
√2 ≈ 1.4142

Therefore, x ≈ 1.5972 x 10^10.

So, the solution to the equation log8(x) + log√2(x) = 14 is x ≈ 1.5972 x 10^10.