PYQ Vault
EbooksTutor

Logarithmic equation that reduces to a quadratic: number or sum of its solutions

This type of question, asked 3 times: 2021 Paper 25, 23 Jan 2026 S2, 8 Apr 2026 S2. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 25

    85
    The number of solutions of the equation log⁡4(x−1)=log⁡2(x−3)\log_{4}(x- 1) =\log_{2}(x- 3) is

  2. Question 2

    23 Jan 2026 S2

    57
    The sum of all the real solutions of the equation log⁡(x+3)(6x2+28x+30)=5−2log⁡(6x+10)(x2+6x+9)\log_{(x + 3)}\left( 6x^{2}+ 28x + 30 \right)= 5 - 2\log_{(6x + 10)}\left( x^{2}+ 6x + 9 \right) is equal to :

    Tap an option to check your answer.

  3. Question 3

    8 Apr 2026 S2

    71
    The sum of squares of all real solution of the equation log⁡(x+1)(2x2+5x+3)=4−log⁡(2x+3)(x2+2x+1)\log_{(x + 1)}\left( 2x^{2} + 5x + 3 \right) = 4 - \log_{(2x + 3)}\left( x^{2} + 2x + 1 \right) is equal to ____\_\_\_\_ .