Higher November 2020 Paper 2 Q12
12 Given that \(\dfrac{3^x}{9^{3x}} = 81\)
find the value of \(x\).
Show clear algebraic working.
(3)
| Scheme | Marks |
|---|---|
\(3^4 = \dfrac{3^x}{9^{3x}}\) or \(81 = \dfrac{3^x}{(3^2)^{3x}}\) or \(9^2 = \dfrac{3^x}{9^{3x}}\) or \(81 = \dfrac{(9^{0.5})^x}{9^{3x}}\) | M1 |
| eg \(4 + 6x = x\) or \(4 = x - 2(3x)\) oe or eg \(2 = 0.5x - 3x\) oe | M1 |
| Working required Answer: \(-0.8\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: replacing 81 with \(3^4\) or \(9^{3x}\) with \((3^2)^{3x}\) (or \(3^{6x}\)) or replacing 81 with \(9^2\) or \(3^x\) with \((9^{0.5})^x\) (in an equation)
M1: a correct equation using powers
A1: oe, dep on at least M1