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2. (a) Sketch the curve with equation y = 4 stating any points of intersection with the coordinate axes - Edexcel - A-Level Maths Pure - Question 5 - 2022 - Paper 2

Question 5

2. (a) Sketch the curve with equation y = 4 stating any points of intersection with the coordinate axes. (b) Solve 4^x = 100 giving your answer to 2 dec... show full transcript

Worked Solution & Example Answer:2. (a) Sketch the curve with equation y = 4 stating any points of intersection with the coordinate axes - Edexcel - A-Level Maths Pure - Question 5 - 2022 - Paper 2

Step 1

Sketch the curve with equation y = 4

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Answer

The equation $y = 4$ represents a horizontal line located at $y = 4$ in the Cartesian plane. It intersects the y-axis at the point (0, 4).

The line does not intersect the x-axis, as it is parallel to it, indicating there are no points of intersection with the x-axis. Thus, the only point of intersection with the coordinate axes is at (0, 4). The sketch should reflect the horizontal nature of this line.

Step 2

Solve 4^x = 100

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Answer

To solve the equation $4^x = 100$ , we can take logarithms on both sides.

Using logarithm base 4, we have:

$x = rac{ ext{log} 100}{ ext{log} 4}$

Using the change of base formula:

$ext{log} 100 = ext{log}_{10} 100 = 2$ $ext{log} 4 = ext{log}_{10} 4 \approx 0.602$

Thus, we substitute these values:

$x = rac{2}{0.602} \approx 3.32$

Therefore, the solution to two decimal places is:

$x \approx 3.32$

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