Solve `log_2 x-3/log_2 x=2` (3 marks)
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`x=8\ \ text(or)\ \ 1/2`
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IMPORTANT: Students should recognise this equation as a quadratic, and the best responses substituted `log_2 x` with a variable such as `X`.
| `log_2 x-3/(log_2 x)` | `=2` |
| `(log_2 x)^2-3` | `=2log_2 x` |
| `(log_2 x)^2-2log_2 x-3` | `=0` |
| `text(Let)\ X=log_2 x` | |
| `:.\ X^2-2X-3` | `=0` |
| `(X-3)(X+1)` | `=0` |
MARKER’S COMMENT: Many responses incorrectly stated that there is no solution to `log_2 x=-1` or could not find `x` given `log_2 x=3`.
| `X` | `=3` | `\ \ \ \ \ \ \ \ \ \ ` | `X` | `=-1` |
| `log_2 x` | `=3` | `\ \ \ \ \ \ \ \ \ \ ` | `log_2 x` | `=-1` |
| `x` | `=2^3=8` | `\ \ \ \ \ \ \ \ \ \ ` | `x` | `=2^{-1}=1/2` |
`:.x=8\ \ text(or)\ \ 1/2`