O-LevelAdditional MathematicsLogarithmic and exponential functions4037/12 · May/June 2018 · Q99 Marks
Solve lgx = 3.
- (a)(i)Solve lgx = 3.[1]
- (a)(ii)Write lga - 2lgb + 3 as a single logarithm.[3]
- (b)(i)Solve x - 5 + 6/x = 0.[2]
- (b)(ii)Hence, showing all your working, find the values of a such that log₄a - 5 + 6/log₄a = 0.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- B1 1000
- M1 for use of power rule
- M1dep for addition or subtraction rule
- A1 lg (1000a/b²) Allow lg 10³a/b²
- M1 For attempt to obtain a quadratic equation and solve x² - 5x + 6 = 0
- A1 for both x = 3, x = 2
- M1 For the connection with (i) and attempt to deal with at least one logarithm correctly, either 4^(their 3) or 4^(their 2) (log₄a)² - 5log₄ a + 6 = 0
- A1 a = 64
- A1 a = 16
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