Use the following information. The population of India is currently growing according to the formula P(t) = 1,103.4e0.0149t, where P is the

Good try Anonymous, but, unfortunately, in your answer you forgot the warning about being careful with the units!  P is in millions, so we have:

1103.4*e^0.0149t = 1500

Divide both sides by 1103.4

e^0.0149t = 1500/1103.4

Take log to base e of both sides

0.0149t = ln(1500/1103.4)

Divide both sides by 0.0149

t = ln(1500/1103.4)/0.0149

$${\mathtt{t}} = {\frac{{ln}{\left({\frac{{\mathtt{1\,500}}}{{\mathtt{1\,103.4}}}}\right)}}{{\mathtt{0.014\: \!9}}}} \Rightarrow {\mathtt{t}} = {\mathtt{20.608\: \!643\: \!372\: \!615\: \!506}}$$   years

This is 21 years to the nearest year, so it will be 2005+21 = 2026 when India's population reaches 1500million.

Put 1,500,000,000 in place of P(t) and solve for t. 

Divided 1,500,000,000 by 1,103.4

1,359,434.48= e^0.0149t                 rewrite 0.0149 as the coefficient.

1,359,434.48=0.0149te                    apply ln to both sides to cancel the e

ln(1,359,434.48)=0.0149t                  type it into the calculator as ln(1,359,434.48)/0.0149 to find t