MRSM Trial 2025 Add Maths Paper 1, Question 9Indices, Surds & Logarithms

Solved on video in English · Form 4, Indices, Surds & Logarithms · 5:42 video

The question

(a)

Given aᵐ = aⁿ and m ≠ n, state the value of a.

(b)

Given 27ˣ = √(81ʸ · √9), express y in terms of x.

(c)

Given aᵏ = p and a²ᵏ = q, evaluate log_a (pq)¹/k).

Step 1

If aᵐ = aⁿ but the exponents are different (m ≠ n), the base must be unaffected by the power.

Why this step

We can't set m = n because the question says m ≠ n. So the exponents differ, and the base itself must be special.

2 more steps, each with the reason for it, in the full solution

Final answer

a = 1

Where students lose marks

Watch out: m ≠ n is given, so don't set m = n. Look for the special base where changing the power changes nothing.

5 more steps, each with the reason for it, in the full solution

Final answer

y = (6x − 1)/4

Where students lose marks

Watch out: write everything in base 3, and don't forget √9 = 3¹ adds 1 to the index before the outer root halves it.

4 more steps, each with the reason for it, in the full solution

Final answer

Where students lose marks

Watch out: convert aᵏ = p and a²ᵏ = q to log form first, and don't drop the 1/k when using the power law.

Watch every step of this question solved on video (5:42), with the reason behind each step and a box that checks your own answer.

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