Question

3^(2w) +6 × 3^(w) -27=0
Find w​

Answer 1

`\huge\boxed{w=1}`

Explanation:

`3^(2w)+6*3^w-27=0\\\\\left(3^w\right)^2+6*3^w-27=0\\\\\text{substitute}\ t=3^w>0\\\\t^2+6t-27=0\\\\t^2+9t-3t-27=0\\\\t(t+9)-3(t+9)=0\\\\(t+9)(t-3)=0\iff t+9=0\ \vee\ t-3=0\\\\t+9=0\to t=-9<0\\\\t-3=0\to t=3>0`

therefore

`3^w=3\\\\3^w=3^1\Rightarrow \boxed{w=1}`