SPM 2024 Add Maths Paper 1, Question 5Indices, Surds & Logarithms

Solved on video in English and Bahasa Melayu · Form 4, Indices, Surds & Logarithms · 3:56 video

The question

It is given that log_m p = x and log_n p = y. Using the laws of logarithms, express the following in terms of x and y: log_(m/n) p.

Step 1

Apply the change of base formula: log_(m/n) p = 1 / log_p(m/n).

Why this step

The quotient law only splits the argument, not the base. So we flip to move m/n into the argument first.

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

Final answer

log_(m/n) p = xy / (y − x)

Where students lose marks

Watch out: 1/(1/x − 1/y) is not 1/(1/x) − 1/(1/y). Combine the denominator into one fraction first, then invert it.

Watch every step of this question solved on video (3:56), with the reason behind each step and a box that checks your own answer.

No card. Every past-year question on video, in English and BM.

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