O-LevelAdditional MathematicsLogarithmic and exponential functions4037/22 · May/June 2017 · Q77 Marks
Given that a⁷ = b, where a and b are positive constants, find,
- (a)Given that a⁷ = b, where a and b are positive constants, find,
- (a)(i)log_b a.[1]
- (a)(ii)log_a b.[1]
- (b)Solve the equation log_81 y = -1/4.[2]
- (c)Solve the equation 32^(x²-1) / 4^(x²) = 16.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B1] 1/7
- [B1] 7 or 1/(their 1/7) FT their 7 must not be 1 if following through
- [M1] Anti-logs y = 81^(-1/4) or y = 3⁻¹ or y = 9^(-1/2) oe
- [A1] y = 1/3 only or 0.333[3....] only nfww; implies the M1; y = .... must be seen at least once If M0 then SC1 for e.g. 81^(-1/4) = 1/3 as final answer
- [B1] converts the terms given left hand side to powers of 2 or 4; may have cross-multiplied or separates the power in the numerator correctly or applies a correct log law
- [M1] combines powers and takes logs or equates powers; or brings down all powers for an equation already in logs condone omission of necessary brackets for M1; condone one slip
- [A1] [x =] ±√3 isw cao or ± 1.732050... rot to 3 or more figs. isw
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