2 log(x + a) = log(16a^6), where a is a positive constant
Find x in terms of a, giving your answer in its simplest form - Edexcel - A-Level Maths Pure - Question 9 - 2017 - Paper 3
Question 9
2 log(x + a) = log(16a^6), where a is a positive constant
Find x in terms of a, giving your answer in its simplest form.
(3)
i)
log(9y + b) - log(2y - b) = 2, wh... show full transcript
Worked Solution & Example Answer:2 log(x + a) = log(16a^6), where a is a positive constant
Find x in terms of a, giving your answer in its simplest form - Edexcel - A-Level Maths Pure - Question 9 - 2017 - Paper 3
Step 1
Find x in terms of a
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Answer
To solve for x in the equation 2log(x+a)=log(16a6):
Apply the Power Rule: Rewrite the left side:
log((x+a)2)=log(16a6)
Remove the Logarithms: Set the arguments equal:
(x+a)2=16a6
Take the Square Root: Taking the square root of both sides gives:
x+a=4a3
Isolate x: Solving for x, we get:
x=4a3−a
This simplifies to:
x=a(4a2−1)
Step 2
Find y in terms of b
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Answer
To solve for y in the equation log(9y+b)−log(2y−b)=2:
Apply the Quotient Rule for Logarithms: Combine the logarithms:
log(2y−b9y+b)=2
Remove the Logarithm: Exponentiate both sides:
2y−b9y+b=100
Cross-Multiply: This leads to:
9y+b=100(2y−b)
Expand and Rearrange: Expanding gives:
9y+b=200y−100b
Now rearranging terms results in:
9y+101b=200y
Then,
101b=200y−9y
Isolate y: Finally,
y(200−9)=101b
Leading to:
y=191101b
