SPM 2020 Add Maths Paper 1, Question 8Indices, Surds & Logarithms

Solved on video in English and Bahasa Melayu · 8 marks · Form 4, Indices, Surds & Logarithms · 5:10 video

The question

(a)

Given log_(sqrt 5) x = p, express log_x (sqrt 5) in terms of p.

[4 marks]

(b)

Given log_(sqrt 5) x = p, express log_5 (25x² in terms of p.

[4 marks]

Step 1

Use change of base: log_x (sqrt 5) = 1 / log_(sqrt 5) x.

Why this step

The given is in base √5, so we switch to base √5. The top, log_(√5) √5, is a log of its own base, so it is 1.

1 more step, with the reason for it, in the full solution

Final answer

log_x (√5) = 1/p

Where students lose marks

Watch out: log_(√5) √5 = 1, since any log of its own base is 1. Don't leave the answer as log_(√5) √5 / p.

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

Final answer

log_5 (25x²) = 2 + p

Where students lose marks

Watch out: change log_(√5) x to base 5 to get 2 log_5 x = p. Then log_5 x² is exactly p, not p/2.

Watch every step of this question solved on video (5:10), with the reason behind each step and a box that checks your own answer.

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