SPM 2023 Add Maths Paper 1, Question 9Indices, Surds & Logarithms

Solved on video in English and Bahasa Melayu · Form 4, Indices, Surds & Logarithms · 5:49 video

The question

(a)

It is given that 2^x = 8^y = √(2³z)). Find x : y : z.

(b)

It is given that 9²pq+1) + 3⁴pq−3) = 732. Express p in terms of q.

(c)

Find the value of 1/(log_a ab) + 1/(log_b ab).

Step 1

Convert everything to base 2. From 2^x = 8^y: 8^y = (2³)^y = 2³y), so x = 3y, giving x/y = 3/1, i.e. x : y = 3 : 1.

Why this step

Once all three quantities are powers of 2, we can compare exponents directly. That turns messy powers into simple equations like x = 3y.

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

Final answer

x : y : z = 3 : 1 : 2

Where students lose marks

Watch out: after converting to base 2, join the ratios using a common x. Don't end up with 2 : 6 : 3.

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

Final answer

p = 1/q

Where students lose marks

Watch out: you can't take logs of a sum term by term. Factor out 3⁴pq) using the index laws first.

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

Final answer

Where students lose marks

Watch out: changing the base is only half the job. Add the logs with the product law until you get log_(ab)(ab) = 1.

Watch every step of this question solved on video (5:49), with the reason behind each step and a box that checks your own answer.

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