A-Level Edexcel Maths Pure Trigonometric Equations: Find the exact value of $x$ for

Find the exact value of $x$ for which $$ ext{log}_2(2x) = ext{log}_2(5x + 4) - 3$$ Given that $$ ext{log}_b(y) + 3 ext{log}_2(2) = 5$$ express $y$ in terms of $a$ - Edexcel - A-Level Maths Pure - Question 8 - 2013 - Paper 4

Question 8

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Find the exact value of $x$ for which $$ ext{log}_2(2x) = ext{log}_2(5x + 4) - 3$$ Given that $$ ext{log}_b(y) + 3 ext{log}_2(2) = 5$$ express $y$ in terms of $... show full transcript

Worked Solution & Example Answer:Find the exact value of $x$ for which $$ ext{log}_2(2x) = ext{log}_2(5x + 4) - 3$$ Given that $$ ext{log}_b(y) + 3 ext{log}_2(2) = 5$$ express $y$ in terms of $a$ - Edexcel - A-Level Maths Pure - Question 8 - 2013 - Paper 4

Step 1

Find the exact value of $x$ for which log_2(2x) = log_2(5x + 4) - 3

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Answer

To solve for $x$ , start by isolating the logarithmic terms:

Rewrite the equation: $ext{log}_2(2x) + 3 = ext{log}_2(5x + 4)$
Use the property of logarithms that allows you to combine them: $ext{log}_2(2x) + ext{log}_2(8) = ext{log}_2(5x + 4)$
Apply the addition property of logarithms: $ext{log}_2(16x) = ext{log}_2(5x + 4)$
Set the arguments equal to each other: $16x = 5x + 4$
Rearrange to solve for $x$ : $16x - 5x = 4$ $11x = 4$ $x = rac{4}{11}$

Step 2

Given that log_b(y) + 3log_2(2) = 5 express y in terms of a

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Answer

Start by isolating $y$ :

Rewrite the equation using properties of logarithms: $ext{log}_b(y) = 5 - 3 ext{log}_2(2)$
Simplifying gives: $ext{log}_b(y) = 5 - 3$ (since $log_2(2) = 1$ ) $ext{log}_b(y) = 2$
Convert the logarithmic equation to exponential form: $y = b^2$
If we express $b$ in terms of $a$ , we get: $y = a^2$

Thus, $y$ is expressed in terms of $a$ as: $y = a^2$

Find the exact value of $x$ for which $$ ext{log}_2(2x) = ext{log}_2(5x + 4) - 3$$ Given that $$ ext{log}_b(y) + 3 ext{log}_2(2) = 5$$ express $y$ in terms of $a$ - Edexcel - A-Level Maths Pure - Question 8 - 2013 - Paper 4

Worked Solution & Example Answer:Find the exact value of $x$ for which $$ ext{log}_2(2x) = ext{log}_2(5x + 4) - 3$$ Given that $$ ext{log}_b(y) + 3 ext{log}_2(2) = 5$$ express $y$ in terms of $a$ - Edexcel - A-Level Maths Pure - Question 8 - 2013 - Paper 4

Find the exact value of $x$ for which log_2(2x) = log_2(5x + 4) - 3

Given that log_b(y) + 3log_2(2) = 5 express y in terms of a

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