27^(x-2/3)-9^(x-1)-2*3^(2x-1)-2*3^(3x-1)=0

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вопрос

We need to simplify and solve the given equation:

27^(x-2/3) - 9^(x-1) - 23^(2x-1) - 23^(3x-1) = 0

Rewrite in terms of powers of 3:

(3^3)^(x-2/3) - (3^2)^(x-1) - 2(3^(2x)) - 2(3^(3x)) = 0

3^(3x-2) - 3^(2x-2) - 23^(2x) - 23^(3x) = 0

Now, let's solve for x:

3^(3x-2) - 3^(2x-2) - 23^(2x) - 23^(3x) = 0

Since all terms have a common base of 3, we can combine them:

3^(2x-2)(3^(x) - 1) - 2*3^2x(3^(x) + 1) = 0

Factor out 3^(x) from the common terms:

3^(x)(3^x(3^(x-2) - 1) - 2*3^(x)(3 + 1)) = 0

3^(x)(3^3 - 1 - 234) = 0

3^(x)(27 - 1 - 24) = 0

3^(x)(2) = 0

This equation does not have a real solution since 3^(x) cannot be equal to 0. Therefore, there is no real x that satisfies the given equation.