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Given $$ 2^2 \times 4^y = \frac{1}{2 \sqrt{2}} $$ express y as a function of x. - Edexcel - A-Level Maths Pure - Question 3 - 2019 - Paper 2

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Given--$$-2^2-\times-4^y-=-\frac{1}{2-\sqrt{2}}-$$--express-y-as-a-function-of-x.-Edexcel-A-Level Maths Pure-Question 3-2019-Paper 2.png

Given $$ 2^2 \times 4^y = \frac{1}{2 \sqrt{2}} $$ express y as a function of x.

Worked Solution & Example Answer:Given $$ 2^2 \times 4^y = \frac{1}{2 \sqrt{2}} $$ express y as a function of x. - Edexcel - A-Level Maths Pure - Question 3 - 2019 - Paper 2

Step 1

Express in powers of 2

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Answer

Rewriting the equation in powers of 2:

22×(22)y=1222^2 \times (2^2)^y = \frac{1}{2 \sqrt{2}}

This simplifies to:

22+2y=123/22^{2 + 2y} = \frac{1}{2^{3/2}}

Step 2

Set the exponents equal

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Answer

Now, since the bases are the same, we can set the exponents equal:

2+2y=−322 + 2y = -\frac{3}{2}

Step 3

Solve for y

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Answer

Rearranging yields:

2y=−32−22y = -\frac{3}{2} - 2

This simplifies to:

2y=−32−42=−722y = -\frac{3}{2} - \frac{4}{2} = -\frac{7}{2}

Dividing by 2 gives:

y=−74y = -\frac{7}{4}

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