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Find `x` given `100^(x-2) = 1000^x`. (2 marks)
`-4`
| `100^(x-2)` | `= 1000^x` |
| `(10^2)^(x-2)` | `= (10^3)^x` |
| `10^(2x-4)` | `= (10)^(3x)` |
| `2x-4` | `=3x` |
| `:. x` | `= -4` |
Solve the equation `2^(3x-3) = 8^(2-x)` for `x`. (2 marks)
`3/2`
| `2^(3x-3)` | `= 2^(3(2-x))` |
| `3x-3` | `= 6-3x` |
| `6x` | `= 9` |
| `:. x` | `= 3/2` |
Solve the equation `3^(-4x) = 9^(6-x)` for `x.` (2 marks)
`-6`
| `3^(-4x)` | `= (3^2)^(6-x)` |
| `3^(-4x)` | `=3^(12-2x)` |
| ` -4x` | `= 12-2x` |
| `2x` | `=-12` |
| `:. x` | `=-6` |
Solve `2^(2x+1)=32`. (2 marks)
`x=2`
| `2^(2x+1)` | `=32` |
| `2^(2x+1)` | `=2^5` |
| `2x+1` | `=5` |
| `:. x` | `=2` |