A-LevelMathematicsLogarithmic and exponential functions9709/32 · May/June 2019 · Q24 Marks

Showing all necessary working, solve the equation 9ˣ = 3ˣ + 12. Give your answer correct to 2 decimal places.

Showing all necessary working, solve the equation 9ˣ = 3ˣ + 12. Give your answer correct to 2 decimal places.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[B1] State or imply u² - u - 12 (= 0), or equivalent in 3ˣ (Need to be convinced they know 3^(2x) = (3ˣ)²)
[B1] Solve for u, or for 3ˣ, and obtain root 4
[M1] Use a correct method to solve an equation of the form 3ˣ = a where a > 0 (Need to see evidence of method. Do not penalise an attempt to use the negative root as well. e.g. x ln 3 = ln a, x = log₃ a. If seen, accept solution of straight forward cases such as 3ˣ = 3, x = 1 without working)
[A1] Obtain final answer x ≈ 1.26 only (The Q asks for 2 dp)

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Topic: Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, May/June 2019 Paper 3 Variant 2, question 2.

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