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Solve the exponential equation for x. {:[((625)/(256))^(5x-4)=1],[x=]:}

Solve the exponential equation for x x .\newline(625256)5x−4=1x=□ \begin{array}{l} \left(\frac{625}{256}\right)^{5 x-4}=1 \\ x=\square \end{array}

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Full solution

Q. Solve the exponential equation for x x .\newline(625256)5x−4=1x=□ \begin{array}{l} \left(\frac{625}{256}\right)^{5 x-4}=1 \\ x=\square \end{array}
  1. Write Equation: Write down the given exponential equation.\newline(625256)5x−4=1\left(\frac{625}{256}\right)^{5x-4} = 1
  2. Set Exponent to 00: Recognize that any non-zero number raised to the power of 00 is equal to 11. So, we can set the exponent in the equation equal to 00 to solve for xx. 5x−4=05x - 4 = 0
  3. Solve for x: Solve the equation for x.\newlineAdd 44 to both sides of the equation:\newline5x−4+4=0+45x - 4 + 4 = 0 + 4\newline5x=45x = 4
  4. Isolate x: Divide both sides of the equation by 55 to isolate x.\newline5x5=45\frac{5x}{5} = \frac{4}{5}\newlinex=45x = \frac{4}{5}

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