| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | September |
| Marks | 4 |
| Topic | Laws of Logarithms |
| Type | Evaluate log expression using laws |
| Difficulty | Moderate -0.8 This is a straightforward application of logarithm laws (power rule, subtraction/addition rules) followed by a simple equation to solve for the base. The algebraic manipulation is routine and the final step requires only basic understanding that log_a(x) = 3/2 means a^(3/2) = x. No problem-solving insight needed, just mechanical application of standard rules. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules |
4.\\
(a) (i) Express as a single logarithm
$$\log _ { a } 36 - \frac { 1 } { 2 } \log _ { a } 81 + 2 \log _ { a } 4 - 3 \log _ { a } 2$$
(a) (ii) Hence find the value of $a$, given
$$\log _ { a } 36 - \frac { 1 } { 2 } \log _ { a } 81 + 2 \log _ { a } 4 - 3 \log _ { a } 2 = \frac { 3 } { 2 }$$
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q4 [4]}}