OCR MEI C2 2006 June — Question 9 4 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2006
SessionJune
Marks4
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Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeSolve exponential equation using logarithms
DifficultyModerate -0.8 This is a straightforward logarithmic equation requiring only taking logs of both sides, applying the power rule, and solving for x. It's a standard textbook exercise testing basic logarithm manipulation with no problem-solving insight required, making it easier than average but not trivial since students must execute the technique correctly.
Spec1.06g Equations with exponentials: solve a^x = b
Use logarithms to solve the equation \(5^{3x} = 100\). Give your answer correct to 3 decimal places. [4]
AnswerMarks Guidance
\(3x \log 5 = \log 100\)M1 allow any or no base or \(3x = \log_5 100\)
\(3x = \log 100/\log 5\)M1 dep't
\(x = 0.954\)A2 A1 for other rot versions of 0.9537...; SC B2/4 for 0.954 with no log wkg; SC B1 r.o.t. 0.9537... 
$3x \log 5 = \log 100$ | M1 | allow any or no base or $3x = \log_5 100$ |
$3x = \log 100/\log 5$ | M1 | dep't |
$x = 0.954$ | A2 | A1 for other rot versions of 0.9537...; SC B2/4 for 0.954 with no log wkg; SC B1 r.o.t. 0.9537... | $4$ | $19$ |
Use logarithms to solve the equation $5^{3x} = 100$. Give your answer correct to 3 decimal places. [4]

\hfill \mbox{\textit{OCR MEI C2 2006 Q9 [4]}}
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