A-Level Edexcel Maths Pure Integration: 3. (a) Given that 2log(4−x)=log(

3. (a) Given that 2log(4−x)=log(x+8) show that x2−9x+8=0 (b) (i) Write down the roots of the equation x2−9x+8=0 (ii) State which of the roots in (b)(i) is not a solution of 2log(4−x)=log(x+8) giving a reason for your answer. - Edexcel - A-Level Maths Pure - Question 6 - 2020 - Paper 2

Question 6

3.-(a)-Given-that-2log(4−x)=log(x+8)-show-that--x2−9x+8=0--(b)-(i)-Write-down-the-roots-of-the-equation--x2−9x+8=0--(ii)-State-which-of-the-roots-in-(b)(i)-is-not-a-solution-of-2log(4−x)=log(x+8)-giving-a-reason-for-your-answer.-Edexcel-A-Level Maths Pure-Question 6-2020-Paper 2.png

3. (a) Given that 2log(4−x)=log(x+8) show that x2−9x+8=0 (b) (i) Write down the roots of the equation x2−9x+8=0 (ii) State which of the roots in (b)(i) is not a ... show full transcript

Worked Solution & Example Answer:3. (a) Given that 2log(4−x)=log(x+8) show that x2−9x+8=0 (b) (i) Write down the roots of the equation x2−9x+8=0 (ii) State which of the roots in (b)(i) is not a solution of 2log(4−x)=log(x+8) giving a reason for your answer. - Edexcel - A-Level Maths Pure - Question 6 - 2020 - Paper 2

Step 1

Given that 2log(4−x)=log(x+8) show that

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Answer

To prove that the equation $x^2 - 9x + 8 = 0$ is valid, start with the given equation:

Begin by rearranging the logarithmic equation:

$2log(4 - x) = log(x + 8)$

This can be rewritten using the properties of logarithms:

$log((4 - x)^2) = log(x + 8)$

Since the logarithms are equal, the arguments must also be equal:

$(4 - x)^2 = x + 8$
Expand the left side:

$(4 - x)(4 - x) = 16 - 8x + x^2$
Set the equation to zero:

$16 - 8x + x^2 = x + 8$ $x^2 - 9x + 8 = 0$

This proves the equation as required.

Step 2

(b) (i) Write down the roots of the equation

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Answer

To find the roots of the quadratic equation $x^2 - 9x + 8 = 0$ , we can factor it:

$x^2 - 9x + 8 = (x - 1)(x - 8) = 0$

From this, the roots are:

$x = 1$
$x = 8$

Step 3

(b) (ii) State which of the roots in (b)(i) is not a solution of 2log(4−x)=log(x+8) giving a reason for your answer.

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Answer

To determine which root is not a solution of $2log(4 - x) = log(x + 8)$ , we substitute the roots $x = 1$ and $x = 8$ back into the logarithmic equation:

When $x = 1$ : $2log(4 - 1) = log(1 + 8)$ $2log(3) = log(9)$ This is true as $log(9) = 2log(3)$ .
When $x = 8$ : $2log(4 - 8) = log(8 + 8)$ $2log(-4) = log(16)$ Here, $log(-4)$ is undefined.

Thus, the root $x = 8$ is not a solution because the logarithm of a negative number is not defined.

3. (a) Given that 2log(4−x)=log(x+8) show that x2−9x+8=0 (b) (i) Write down the roots of the equation x2−9x+8=0 (ii) State which of the roots in (b)(i) is not a solution of 2log(4−x)=log(x+8) giving a reason for your answer. - Edexcel - A-Level Maths Pure - Question 6 - 2020 - Paper 2

Given that 2log(4−x)=log(x+8) show that

(b) (i) Write down the roots of the equation

(b) (ii) State which of the roots in (b)(i) is not a solution of 2log(4−x)=log(x+8) giving a reason for your answer.

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