To solve for t...

400,000 = 2^{t/5}

Take the log of both sides.

log(400,000) = log(2^{t/5})

Rewrite as

log(400,000) = (t/5) * log(2)

Divide both sides by log(2).

log(400,000) / log(2) = t/5

Multiply both sides by 5.

5log(400,000) / log(2) = t

93.048 ≈ t