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secondary 3 | A Maths
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log₅(x²-5x+20) = 1/log₂5 + 1/log₇5
=> log₅(x²-5x+20) = log2/log5 + log7/log5
=> log₅(x²-5x+20) = log₅2 + log₅7
=> log₅(x²-5x+20) = log₅14
=> x²-5x+20 = 14
=> x²-5x+6 = 0
=> (x-2)(x-3) = 0
=> x = 2 or 3
(a)(ii)
lg y² = (lg y)²
=> 2lg y = (lg y)²
=> (lg y)² - 2lg y = 0
=> lg y(lg y-2) = 0
=> lg y = 0 or lg y - 2 = 0
=> y = 1 or lg y = 2
=> y = 1 or y = 100
(b)
8e⁴ˣ - 15e²ˣ - 2 = 0
=> 8(e²ˣ)² - 15e²ˣ - 2 = 0
=> (8e²ˣ + 1)(e²ˣ - 2) = 0
=> e²ˣ = -1/8 (n.a.) or e²ˣ = 2
=> e²ˣ = 2
=> 2x = ln 2
=> x = (ln 2)/2 = 0.347
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