Given \(m\) and \(n\) are positive constants, which expression is equal to
\(\log _m x^5=n\)
- \(x=n^{\small{\dfrac{m}{5}}}\)
- \(x=m^{\small{\dfrac{n}{5}}}\)
- \(x=\dfrac{n^m}{5}\)
- \(x=\dfrac{m^n}{5}\)
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Given \(m\) and \(n\) are positive constants, which expression is equal to
\(\log _m x^5=n\)
\(\Rightarrow B\)
\(\log _m x^5=n\)
\(\text{By definition:}\)
\(x^5=m^n\)
\(x=\left(m^n\right)^{\small{\dfrac{1}{5}}}=m^{\small{\dfrac{n}{5}}}\)
\(\Rightarrow B\)
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`
Solve the equation `lnx=2`. Give you answer correct to four decimal places. (2 marks)
`7.3891`
| `ln x` | `=2` |
| `log_e x` | `=2` |
| `x` | `=e^2` |
| `=7.38905…` | |
| `=7.3891\ \ text{(to 4 d.p.)}` |