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Sum of the roots of an exponential equation that is a quadratic in a^x

This type of question, asked 4 times: 2021 Paper 23, 14 Jun 2022, 27 Jun 2022, 8 Apr 2024. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 23

    73
    The sum of the roots of the equation x+1−2log⁡2(3+2x)+2log⁡4(10−2−x)=0x + 1 - 2\log_{2}\left( 3 +2^{x} \right)+ 2\log_{4}\left( 10 -2^{- x} \right)= 0, is:

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  2. Question 2

    14 Jun 2022

    152
    The sum of all the real roots of the equation (e2x−4)(6e2x−5ex+1)=0\left( e^{2x}- 4 \right)\left( 6e^{2x}- 5e^{x}+ 1 \right)= 0 is

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  3. Question 3

    27 Jun 2022

    82
    If the sum of all the roots of the equation e2x−11ex−45e−x+812=0e^{2x}- 11e^{x}- 45e^{-x}+\frac{81}{2}= 0 is log⁡eP\log_{e}P, then pp is equal to

  4. Question 4

    8 Apr 2024

    62
    The sum of all the solutions of the equation (8)2x−16⋅(8)x+48=0(8)^{2x}- 16 \cdot (8)^{x}+ 48 = 0 is :

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