Pre-U Pre-U 9794/1 2010 June — Question 1 3 marks

Exam BoardPre-U
ModulePre-U 9794/1 (Pre-U Mathematics Paper 1)
Year2010
SessionJune
Marks3
TopicLaws of Logarithms
TypeSolve exponential equation using logarithms
DifficultyEasy -1.2 This is a straightforward exponential equation requiring only the recognition that 4 = 2^2, leading to 2^x = 2^(4x+2), then equating exponents to get x = 4x + 2, solving to x = -2/3. It's a routine single-technique question worth 3 marks with no conceptual difficulty, making it easier than average.
Spec1.06g Equations with exponentials: solve a^x = b

Solve the equation \(2^x = 4^{2x+1}\). [3]

AnswerMarks Guidance
Write 4 as a power of 2M1
Write a linear eqnM1
\(x = -\frac{2}{3}\) or decimal equiv rounding to 0.667A1 [3]
OR
AnswerMarks Guidance
Indicate the logs should be taken of both sidesM1
Use the third log law to remove powersDM1
\(x = -\frac{2}{3}\) or decimal equiv rounding to 0.667A1
Answer only 3/3 [3]
Write 4 as a power of 2 | M1 | 
Write a linear eqn | M1 |
$x = -\frac{2}{3}$ or decimal equiv rounding to 0.667 | A1 | [3]

OR

Indicate the logs should be taken of both sides | M1 |
Use the third log law to remove powers | DM1 |
$x = -\frac{2}{3}$ or decimal equiv rounding to 0.667 | A1 |
Answer only 3/3 | | [3]
Solve the equation $2^x = 4^{2x+1}$. [3]

\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2010 Q1 [3]}}