Question 7 - A-Level Maths

Exam Board	OCR MEI
Module	C2 (Core Mathematics 2)
Year	2010
Session	June
Marks	2
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Laws of Logarithms
Type	Combine logs into single logarithm
Difficulty	Easy -1.2 This is a straightforward application of two basic logarithm laws: the power rule and addition of logarithms. It requires only algebraic manipulation (converting √x to x^(1/2), then combining exponents) with no problem-solving insight, making it easier than average but not trivial since students must recognize and correctly apply multiple rules.
Spec	1.06f Laws of logarithms: addition, subtraction, power rules

Express \(\log_a x^3 + \log_a \sqrt{x}\) in the form \(k \log_a x\). [2]

Answer	Marks	Guidance
\(3.5 \log_a x\) or \(k = 3.5\)	2 marks	B1 for \(3 \log_a x\) or \(\frac{1}{2} \log_a x\) or \(\log_a x^{3\frac{1}{2}}\) seen

$3.5 \log_a x$ or $k = 3.5$ | 2 marks | B1 for $3 \log_a x$ or $\frac{1}{2} \log_a x$ or $\log_a x^{3\frac{1}{2}}$ seen

Express $\log_a x^3 + \log_a \sqrt{x}$ in the form $k \log_a x$. [2]

\hfill \mbox{\textit{OCR MEI C2 2010 Q7 [2]}}