- A student's attempt to solve the equation \(2 \log _ { 2 } x - \log _ { 2 } \sqrt { x } = 3\) is shown below.
$$\begin{aligned}
& 2 \log _ { 2 } x - \log _ { 2 } \sqrt { x } = 3
& 2 \log _ { 2 } \left( \frac { x } { \sqrt { x } } \right) = 3
& 2 \log _ { 2 } ( \sqrt { x } ) = 3
& \log _ { 2 } x = 3
& x = 3 ^ { 2 } = 9
\end{aligned}$$
using the subtraction law for logs simplifying using the power law for logs using the definition of a log
- Identify two errors made by this student, giving a brief explanation of each.
- Write out the correct solution.