Explicação passo-a-passo:
[tex]l(t) = 3000 \times {1.5}^{t } \\ 54000 = 3000 \times {1.5}^{t} \\ log(54000) = log(3000) + log( {1.5}^{t} ) \\ \\ 4.73 = 3.48 + t log( \frac{3}{2} ) \\ 4.73 = 3.48 + t log(3) - t log(2) \\ 4.73 = 3.48 + 0.477t - 0.301t \\ 4.73 - 3.48 = 0.176t \\ 1.25 = 0.176t \\ t = \frac{1.25}{0.176} \\ \\ t = 7.1 \: \: meses[/tex]
