Pearson Edexcel IAL Mathematics P2.5.3 Solving equations using logarithms

Practise solving exponential and logarithmic equations with substitutions, change of base and model equations needing rounded answers.

Exam points

take logs of both sides to solve a^x=b or model equations for time
give exact log-form coordinates or rounded model values as required by the question

[Maximum number: 3]

In this question you must show all stages of your working.

Solutions relying on calculator technology are not acceptable.

Hence solve

2 \times 4^{x}-2^{x+3}=17 \times 2^{x-1}-4

$4p^2-33p+8=0\Rightarrow(4p-1)(p-8)=0$ $p=\frac14$ or 8 $2^x=\frac14\Rightarrow x=-2;\quad 2^x=8\Rightarrow x=3$ x=-2, 3

M1 M1 A1

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