Exponential growth and decay, question 11

A colony has population $P(t)$ thousand after $t$ hours, given below. A student finds its doubling time as shown. Find the first line that is wrong.

P(t) = 3e^{0.4t}

$6 = 3e^{0.4t}$
Set P equal to twice the starting value.
$\log 6 = \log 3 + 0.4t$
Take logarithms: log(ab) = log a + log b, and log(e^0.4t) = 0.4t.
$\log 6 - \log 3 = \log 3$
A difference of logarithms is the logarithm of the difference, log(6 − 3).
$t = \frac{\log 3}{0.4} \approx 2.75$
Solve for t, in hours.

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