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secondary 3 | A Maths

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2²ˣ⁻⁴ x 40 = 5²⁻ˣ

=> 4ˣ x 2⁻⁴ x 40 = 5² x 5⁻ˣ

=> 4ˣ x 1/16 x 40 = 25 x 1/5ˣ

=> 4ˣ x 1/2 = 5 x 1/5ˣ

=> 4ˣ = 10 x 1/5ˣ

=> 4ˣ x 5ˣ = 10

=> (4 x 5)ˣ = 10

=> 20ˣ = 10

(b)

5ˣ⁻¹ + 5²⁻ˣ = 6

=> 5ˣ/5 + 25/5ˣ = 6

subst. u = 5ˣ ;

=> u/5 + 25/u = 6

=> u² + 125 = 30u

=> u² - 30u + 125 = 0

=> (u - 5)(u - 25) = 0

=> u = 5 or u = 25

=> 5ˣ = 5¹ or 5ˣ = 5²

=> x = 1 or x = 2

...

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