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Rewrite the base on the left side of the equation so it matches the base on the right side.

Chemistry

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Answer

x=35x = \frac{3}{5}

Step-by-step solution

5 steps

  1. Rewrite the base on the left side of the equation so it matches the base on the right side.

    The equation is given as:

    (1/4)x=23x−3(1/4)^x = 2^{3x-3}

    We know that 1/41/4 can be written as 2−22^{-2}.

  2. Substitute 2−22^{-2} for 1/41/4 in the equation.

    (2−2)x=23x−3(2^{-2})^x = 2^{3x-3}

  3. Apply the exponent rule (am)n=amn(a^m)^n = a^{mn} to the left side.

    2−2x=23x−32^{-2x} = 2^{3x-3}

  4. Since the bases are now the same, equate the exponents.

    −2x=3x−3-2x = 3x-3

  5. Solve the linear equation for xx.

    Add 2x2x to both sides of the equation:

    0=3x+2x−30 = 3x + 2x - 3 0=5x−30 = 5x - 3

    Add 3 to both sides:

    3=5x3 = 5x

    Divide by 5:

    x=35x = \frac{3}{5}

    The value of xx is 35\frac{3}{5}.

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