Kay's Math: Analysis and approaches IB math-HL- Logarithm and exponential

$1\cdot Solve\; for \; x\; \log _{2}\left (x^{2}-2x+1 \right )=1+\log _{2}\left(x-1 \right )$ (3 marks)

$2\cdot Solve\; for \; x\; : 8^{2x+3}=4\sqrt[3]{2}$ (3 marks)

$3\cdot Solve \; simultaneously: 4^{x}=8^{y}\;and \;9^{y}=\frac{243}{3^{x}}$   (6 marks)

$4\cdot Sania \;has\; $5000\; to\; invest\;in\; an\; account\; type\; that\; pays\; 5.2\% \;p.a \;interest compounded annually. Find, using logarithms how long it will take for her investment to reach $20,000.$
  (4 marks)

$5\cdot \;A\; farmer\; monitoring\; an\; insect\; plague\; notices\; that\; the \;area\; affected\; by\;$
$the\; insects\; is \;given\; by\;A= 1000\times 2^ {0.7n} ha,\;$ $where \;n \;is\; the\; number\; of\; weeks\; after\; the \;initial\; observation.$ $\;Estimate\; the \;time \;taken\; for\; the \;affected\; area \;to\; reach\; 5000ha.$ (4 marks)

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Wednesday, October 2, 2019

Analysis and approaches IB math-HL- Logarithm and exponential

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