(a) Evaluate without using tables or calculator: log(base 10)(0.0625) + log(base 10)(160), giving your answer as a whole number. [4 marks]
(b) (i) Show that (2^n * 9^(n+1)) / (6^(2n) * 3^(1-n)) simplifies to 3. [6 marks]
(ii) Hence, or otherwise, find the value of n if (2^n * 9^(n+1)) / (6^(2n) * 3^(1-n)) = 3^(2n-5). [3 marks]
(c) Rationalise the denominator and simplify: (4 + sqrt(5)) / (4 - sqrt(5)), giving your answer in the form a + b*sqrt(5), where a and b are rational numbers. [5 marks]

Question

(a) Evaluate without using tables or calculator: log(base 10)(0.0625) + log(base 10)(160), giving your answer as a whole number. [4 marks]
(b) (i) Show that (2^n * 9^(n+1)) / (6^(2n) * 3^(1-n)) simplifies to 3. [6 marks]
    (ii) Hence, or otherwise, find the value of n if (2^n * 9^(n+1)) / (6^(2n) * 3^(1-n)) = 3^(2n-5). [3 marks]
(c) Rationalise the denominator and simplify: (4 + sqrt(5)) / (4 - sqrt(5)), giving your answer in the form a + b*sqrt(5), where a and b are rational numbers. [5 marks]

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