Solve `log_9 27=x` for `x`. (2 marks)
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Solve `log_9 27=x` for `x`. (2 marks)
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`3/2`
| `log_9 27` | `=x` | |
| `9^x` | `=27\ \ text{(by log definition)}` | |
| `log_10 9^x` | `=log_10 27` | |
| `x log_10 9` | `=log_10 27` | |
| `x` | `=(log_10 27)/(log_10 9)` | |
| `=3/2` |
Solve `log_16 2=x` for `x`. (2 marks)
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`0.25`
| `log_16 2` | `=x` | |
| `16^x` | `=2` | |
| `log_10 16^x` | `=log_10 2` | |
| `x log_10 16` | `=log_10 2` | |
| `x` | `=(log_10 2)/(log_10 16)` | |
| `=0.25` |
Solve the equation `log_9 x=-3/2`. (2 marks)
`x = 1/27`
| `log_9 x` | `=-3/2` | |
| `x` | `=9^(-3/2)` | |
| `=1/(sqrt9)^3` | ||
| `=1/27` |
Solve the equation `log_4 x=3/2`. (2 marks)
`x = 8`
| `log_4 x` | `=3/2` | |
| `x` | `=4^(3/2)` | |
| `=8` |
What is the solution to the equation `log_3(a-1) = -2`? (2 marks)
`a=10/9`
| `log_3 (a-1)` | `= -2` |
| `a-1` | `= 3^{-2}` |
| `a` | `=1/3^2+1` |
| `= 10/9` |
What is the solution to the equation `log_3 x = -1`? (1 mark)
`x=1/3`
| `log_3 x` | `=-1` |
| `x` | `=3^{-1}` |
| `=1/3` |
What is the solution to the equation `log_2(x-1) = 8`?
`D`
| `log_2 (x-1)` | `= 8` |
| `x-1` | `= 2^8` |
| `x` | `= 257` |
`=> D`