Selangor Trial 2025 Add Maths Paper 2, Question 2Indices, Surds & Logarithms

Solved on video in English · Form 4, Indices, Surds & Logarithms · 4:56 video

The question

(a)

(a) Determine whether ⁴√154 is a surd or not. Give your reason.

(b)(i)

(b)(i) Prove that logₐ b = (log_c b) / (log_c a).

(b)(ii)

(b)(ii) Hence, solve log₂ 2x − log₄(3x + 4) = 1.

Step 1

Test whether 154 is a perfect fourth power. 3⁴ = 81 and 4⁴ = 256, so 154 lies between them and is not a perfect fourth power.

Why this step

A surd is a root whose value is irrational. Checking whether 154 is a perfect fourth power tells us if the root could be a whole number.

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

Final answer

Surd, because its value is irrational

Where students lose marks

Watch out: 'it has a root sign' is not a reason. Say the value is irrational (non-terminating, non-recurring decimal).

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

Final answer

Shown

Where students lose marks

Start by letting logₐ b = x and writing aˣ = b, and don't skip the power-law step x log_c a = log_c b.

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

Final answer

x = 1/3 (marking-scheme answer; printed paper shows log₄(3x + 4), see note)

Watch every step of this question solved on video (4:56), with the reason behind each step and a box that checks your own answer.

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