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Solve the exponential equation for x. {:[(2^(3x-4))/(x^(x-5))=2^(8x-1)],[x=]:}

Solve the exponential equation for x x .\newline23x−44x−5=28x−1x=□ \begin{array}{l} \frac{2^{3 x-4}}{4^{x-5}}=2^{8 x-1} \\ x=\square \end{array}

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Full solution

Q. Solve the exponential equation for x x .\newline23x−44x−5=28x−1x=□ \begin{array}{l} \frac{2^{3 x-4}}{4^{x-5}}=2^{8 x-1} \\ x=\square \end{array}
  1. Simplify Equation: First, let's simplify the given exponential equation by isolating the terms with the base of 22 on one side of the equation.\newlineWe have:\newline23x−4xx−5=28x−1\frac{2^{3x-4}}{x^{x-5}} = 2^{8x-1}\newlineSince the bases on both sides of the equation are the same (base 22), we can equate the exponents:\newline3x−4=8x−13x - 4 = 8x - 1
  2. Equate Exponents: Next, we solve for xx by moving the terms involving xx to one side and the constant terms to the other side:\newline3x−8x=−1+43x - 8x = -1 + 4\newline−5x=3-5x = 3
  3. Solve for x: Now, we divide both sides by −5-5 to solve for x:\newlinex=3(−5)x = \frac{3}{(-5)}\newlinex=−35x = -\frac{3}{5}

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