Aussie Maths & Science Teachers: Save your time with SmarterEd
Solve the equation `2 log_2(x + 5)-log_2(x + 9) = 1`. (3 marks)
--- 6 WORK AREA LINES (style=lined) ---
`x = text{−1}`
| `2 log_2(x + 5)-log_2(x + 9)` | `= 1` |
| `log_2(x + 5)^2-log_2(x + 9)` | `= 1` |
| `log_2(((x + 5)^2)/(x + 9))` | `= 1` |
| `((x + 5)^2)/(x + 9)` | `= 2` |
| `x^2 + 10x + 25` | `= 2x + 18` |
| `x^2 + 8x + 7` | `= 0` |
| `(x + 7)(x + 1)` | `= 0` |
`:. x = -1\ \ \ \ (x != text{−7}\ \ text(as)\ \ x > text{−5})`
Which of the following is equal to `(log_2 9)/(log_2 3)`?
`A`
| `(log_2 9)/(log_2 3)` | `= (log_2 3^2)/(log_2 3)` |
| `= (2 log_2 3)/(log_2 3)` | |
| `= 2` |
`=> A`
Write `log 2 + log 4 + log 8 + … + log 512` in the form `a log b` where `a` and `b` are integers greater than `1.` (2 marks)
--- 5 WORK AREA LINES (style=lined) ---
`45 log 2`
`log 2 + log 4 + log 8 + … + log 512`
`= log 2^1 + log 2^2 + log2^3 + … + log 2^9`
`= log 2 + 2 log 2 + 3 log 2 + … + 9 log 2`
`= 45 log 2`