Solve the equation below. \( \log _{2} \sqrt{(x+2)}-\log _{4} x=1 \) If \( \sin A=\frac{5}{13} \) and \( \cos B=\frac{4}{5} \) where A and B are acute angles, determine the values of \( \cos (A-B) \) 5 marks (a)Use binomial theorem to expand \( \sqrt{\frac{3+4 x}{3-4 x}} \) up to the third term, by setting \( x=\frac{1}{64} \) in the expanded form determine the value of \( \sqrt{x} \) (b) The cost of 3 maps, 2 tape measure and 5 plumb bob is ksh. 821 . The cost of 5 maps, 2 tape measure and 7 plumb bob is ksh. 1143 . The cost of 10 maps, 4 tape measure and 5 plumb bob is ksh 1674 . Use Cramer's rule to determine the cost of each type of instrument. (10 marks)
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