OCR MEI C2 2011 June — Question 9 3 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2011
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeEvaluate log expression using laws
DifficultyModerate -0.8 This is a straightforward application of logarithm laws (power rule, addition/subtraction rules) with simple arithmetic. The question requires only mechanical manipulation of logs and simplification, making it easier than average but not trivial since it involves multiple steps and combining rules correctly.
Spec1.06f Laws of logarithms: addition, subtraction, power rules
9 You are given that $$\log _ { a } x = \frac { 1 } { 2 } \log _ { a } 16 + \log _ { a } 75 - 2 \log _ { a } 5 .$$ Find the value of \(x\).
AnswerMarks Guidance
\(\log 16^{1/2}\) or \([=] \log 5^2\) s.o.i.M1 if \(a = 10\) assumed, \(x = 12\) c.a.o. scores B3 www
\(\log(4\times 75)\) or \(\log \frac{75}{25}\) s.o.i.M1 \(x = \frac{4 \times 75}{25}\) implies M1M1
\(x = 12\) wwwA1 
$\log 16^{1/2}$ or $[=] \log 5^2$ s.o.i. | M1 | if $a = 10$ assumed, $x = 12$ c.a.o. scores B3 www
$\log(4\times 75)$ or $\log \frac{75}{25}$ s.o.i. | M1 | $x = \frac{4 \times 75}{25}$ implies M1M1 | no follow through
$x = 12$ www | A1 |
9 You are given that

$$\log _ { a } x = \frac { 1 } { 2 } \log _ { a } 16 + \log _ { a } 75 - 2 \log _ { a } 5 .$$

Find the value of $x$.

\hfill \mbox{\textit{OCR MEI C2 2011 Q9 [3]}}
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Q1 3 Q2 3 Q3 5 Q4 3 Q5 5 Q6 5 Q7 4 Q8 3 Q9 3 Q10 2 Q11 11 Q12 17 Q13 12