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Solve an equation with logarithms to bases that are powers of one number

This type of question, asked 2 times: 9 May 2024 S2, 21 Apr 2025 S2. All 2 questions below, oldest first.

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  1. Question 1

    9 May 2024 S2

    128
    If log⁡2x+log⁡4x+log⁡8x+log⁡16x=2536\log_2 x + \log_4 x + \log_8 x + \log_{16} x = \dfrac{25}{36} and x=2kx = 2^k, then kk is

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  2. Question 2

    21 Apr 2025 S2

    110
    If log⁡3x16+9log⁡273x3=5\sqrt{\log_{3}x^{16}}+ 9\log_{27}\sqrt[3]{\frac{3}{x}}= 5, then x=…x= \ldots.

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