2. (a) Rationalise the denominator and simplify: (4 + √5) / (√5 - 1), leaving your answer in the form p + q√5, where p and q are rational numbers. [5 marks]

(b) (i) Show that log_a(x) = log_b(x) / log_b(a). [3 marks]
(ii) Hence, evaluate log₄(8) + log₈(32) without using tables or calculator. [5 marks]

(c) Solve the equation: 3^(x+1) + 3^(x-1) = 30. [4 marks]

Question

2. (a) Rationalise the denominator and simplify: (4 + √5) / (√5 - 1), leaving your answer in the form p + q√5, where p and q are rational numbers. [5 marks]

(b) (i) Show that log_a(x) = log_b(x) / log_b(a). [3 marks]
    (ii) Hence, evaluate log₄(8) + log₈(32) without using tables or calculator. [5 marks]

(c) Solve the equation: 3^(x+1) + 3^(x-1) = 30. [4 marks]

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