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Express $8^{2x+3}$ in the form $2^n$, stating $y$ in terms of $x$. - Edexcel - A-Level Maths Pure - Question 4 - 2013 - Paper 3

Question 4

$Express-$8^{2x+3}$-in-the-form-$2^n$,-stating-$y$-in-terms-of-$x$.-Edexcel-A-Level Maths Pure-Question 4-2013-Paper 3.png$

Express $8^{2x+3}$ in the form $2^n$, stating $y$ in terms of $x$.

Worked Solution & Example Answer:Express $8^{2x+3}$ in the form $2^n$, stating $y$ in terms of $x$. - Edexcel - A-Level Maths Pure - Question 4 - 2013 - Paper 3

Step 1

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Answer

We start by rewriting 8 in terms of 2:

$8 = 2^3$

Therefore,

$8^{2x+3} = (2^3)^{2x+3}$

Step 2

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Answer

Using the property of exponents, we can simplify this further:

$(2^3)^{2x+3} = 2^{3(2x+3)} = 2^{6x + 9}$

Step 3

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Answer

Now, setting this equal to the form $2^n$ , we get:

$y = 6x + 9$

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