| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2019 |
| Marks | 3 |
| Topic | Laws of Logarithms |
| Type | Simplify or prove logarithmic identity |
| Difficulty | Easy -1.8 This is a straightforward logarithm manipulation exercise requiring only basic log laws (power rule, quotient rule, and addition of logs). It's purely algebraic verification with no problem-solving element—students simply apply standard rules mechanically to show both sides are equal. Worth only 3 marks and significantly easier than typical A-level questions. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules |
Show that
$$\log_a(x^{10}) - 2\log_a\left(\frac{x^3}{4}\right) = 4\log_a(2x)$$
[3]
\hfill \mbox{\textit{SPS SPS FM 2019 Q4 [3]}}