Additional Mathematics – Equations, inequalities and graphs | e-Consult

Set \(t = 2^{y}\) (so \(t>0\)). The equation becomes

\(t^{2}-5t+6=0\).

1. Factorise: \((t-2)(t-3)=0\).
2. Thus \(t=2\) or \(t=3\).
3. Recall \(t=2^{y}\). Solve each:

• If \(2^{y}=2\), then \(y=1\).
• If \(2^{y}=3\), take logarithms: \(y=\log_{2}3=\dfrac{\ln3}{\ln2}\) (approximately \(1.585\)).

Therefore the solutions are \(y=1\) and \(y=\log_{2}3\).