O lvl A Maths: Indices and Logarithms

(a) x^3/2 - 8x^-3/2 = 7

(b) e^2x - 5e^-2x = 4

(c) 2^x+3 = 9

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Answer:

(a)


Substitute y = -1 into y = x^3/2
-1 = x^3/2 (rejected)


Substitute y = -1 into y = x^3/2
8 = x^3/2
2³ = x^3/2
x = 2²
x = 4 (ans)


(b)


Substitute y = -1 into y = e^2x
-1 = e^2x (rejected)


Substitute y = 5 into y = e^2x
5 = e^2x
ln 5 = ln e^2x
1.61 = 2x ln e
2x = 1.61
x = 0.805 (ans)


(c)

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