3.18: Single lg and equation with log base x+1

0606/11/M/J/24 — Question 3 · 9 marks · Log laws, Change of base, Equations

(a)
Write 1+lg⁡(x2−1)−2lg⁡(x−1)1 + \lg(x^{2} - 1) - 2\lg(x - 1), where x>1x > 1, as a single logarithm to base 1010. Give your answer in its simplest form.
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(b)
Solve the equation 4log⁡x+15=9log⁡5(x+1)4\log_{x + 1} 5 = 9\log_{5}(x + 1), giving your answers in the form a+bca + b\sqrt{c} where appropriate, or exact equivalents.
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