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Ответ:

Объяснение:

displaystyle\log_{6x+43}frac{1}{64}=3\\\(6x+43)^3=frac{1}{64}\\\(6x+43)^3=(frac{1}{4})^3\\\6x+43=frac{1}{4}\\24x+172=1\\24x=-171\\x=-frac{171}{24}\\x=-7.125\\\

проверка:

6x+43=6*(-7.125)+43=-42.75+43=0.25=1/4

displaystyle\log_{frac{1}{4}}frac{1}{64} =log_{frac{1}{4}}(frac{1}{4})^3=3 \\   верно

ОТВЕТ: x=-7.125

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