To compare the values of 2^1995 and 5^863, we can take the logarithm of both sides to make the comparison easier.

Taking the logarithm base 10 of both sides, we have:

log(2^1995) < log(5^863)

Using the logarithmic property log(a^b) = b * log(a), we can simplify the equation further:

1995 * log(2) < 863 * log(5)

Now, we can calculate the approximate values of log(2) and log(5):

log(2) ≈ 0.3010
log(5) ≈ 0.6989

Substituting these values into the equation, we have:

1995 * 0.3010 < 863 * 0.6989

601.695 < 602.1987

Since 601.695 is less than 602.1987, we can conclude that 2^1995 is indeed less than 5^863.