| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2022 |
| Session | November |
| Marks | 9 |
| Topic | Laws of Logarithms |
| Type | Evaluate log expression using laws |
| Difficulty | Moderate -0.8 Part (a) requires direct application of basic logarithm laws and index recognition (3³=27, 8^(1/2)=4), which is straightforward recall. Part (b) is a standard exponential equation solved by substituting y=2^x to get a linear equation. Both parts are routine textbook exercises requiring minimal problem-solving, making this easier than average but not trivial since it does require correct application of multiple techniques. |
| Spec | 1.06c Logarithm definition: log_a(x) as inverse of a^x1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
5. (a) Evaluate
$$\log _ { 3 } 27 - \log _ { 8 } 4$$
(b) Solve the equation
$$4 ^ { x } - 3 \left( 2 ^ { x + 1 } \right) = 0$$
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\hfill \mbox{\textit{SPS SPS FM 2022 Q5 [9]}}