Question

Solve this equation. http://d.pr/i/7RDw

(please show your working)

Answer 1

Answer should be: http://d.pr/i/lRJn

Answer 2

apply log ...

Answer 3

\[e^{9a} + 2e^{3a} - 3e^{a} = 300\]
Let \(e^a=y\)
\[y^9+2y^3-3y=300\]
\[y^9=300+3y-2y^3\]
\[ln(y)^9=ln(300+3y-2y^3)\]
\[9ln(y)=ln(300+3y-2y^3)\]
\[ln(y)=\frac{1}{9}ln(300+3y-2y^3)\]
\[ln(e^a)=\frac{1}{9}ln(300+3e^a-2e^{3a})\]
\[a=\frac{1}{9}\ln(300+3e^a-2e^{3a})\]

Answer 4

This is the proving solution, I don't think you can solve for 'a' all at one side.