Edexcel A-Level Mathematics AS P2.5.3 Solving Equations Using Logarithms Questions

Practise Edexcel IAL Mathematics P2.5.3 by taking logarithms, using substitutions where needed, checking valid solutions and reporting exact log forms or correctly rounded values.

Exam points

take logarithms or an equivalent substitution to solve exponential equations for the unknown
use change of base and report exact log forms or correctly rounded solutions

[Maximum number: 2]

Figure 1

\section*{In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.}

Figure 1 shows a sketch of the curve with equation $y=3 \times 2^{-x}$
The point P(k, 300000) lies on the curve.

Use logarithms to find the value of k to 2 decimal places.

Table for Question Edexcel A-Level Mathematics AS P2.5.3 Solving Equations Using Logarithms Questions question 1 — Edexcel A-Level Mathematics AS

The table shows corresponding values of x and y for $y=3 \times 2^{-x}$
The values of y are given to 3 decimal places where appropriate.

$300000=3\times2^{-k}$ $2^{-k}=100000$ $-k=\frac{\log 100000}{\log 2}$ k=-16.61
M1: correct use of logarithms leading to an expression for k or -k.
A1: awrt -16.61.

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Edexcel A-Level Mathematics AS P2.5.3 Solving Equations Using Logarithms Questions question 1