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Find the exact value of x for which log₂(2x) = log₅(5x + 4) - 3 Given that logₐ(y) + 3log₂(2) = 5 express y in terms of a - Edexcel - A-Level Maths Pure - Question 5 - 2013 - Paper 4

Question 5

Find the exact value of x for which log₂(2x) = log₅(5x + 4) - 3 Given that logₐ(y) + 3log₂(2) = 5 express y in terms of a. Give your answer in its simplest form.

Worked Solution & Example Answer:Find the exact value of x for which log₂(2x) = log₅(5x + 4) - 3 Given that logₐ(y) + 3log₂(2) = 5 express y in terms of a - Edexcel - A-Level Maths Pure - Question 5 - 2013 - Paper 4

Step 1

Given that logₐ(y) + 3log₂(2) = 5 express y in terms of a.

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Answer

Starting with:

log_a(y) + 3 log_2(2) = 5

Knowing that log₂(2) = 1, we rewrite:

log_a(y) + 3 = 5

Subtracting 3 from both sides gives:

log_a(y) = 2

This implies:

y = a^2

Thus, y expressed in terms of a is:

y = a^2

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