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$Solve the exponential equation for x. {:[64^(7x-8)=1],[x=]:}$

Solve the exponential equation for $x$ . $\newline$ $\begin{array}{l} 64^{7 x-8}=1 \\ x= \end{array}$

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Evaluate exponential functions

Full solution

Q. Solve the exponential equation for

x

.

\newline

\begin{array}{l} 64^{7 x-8}=1 \\ x= \end{array}

Identify Equation and Value: Identify the exponential equation and the value we want to solve for. $\newline$ The equation is $64^{7x-8} = 1$ . We want to solve for $x$ .
Recognize Exponent Rule: Recognize that any non-zero number raised to the power of $0$ is $1$ . So, we can set the exponent of $64$ equal to $0$ to find the value of $x$ . $64^{7x-8} = 1$ implies $7x - 8 = 0$
Solve for x: Solve the equation $7x - 8 = 0$ for $x$ . $\newline$ Add $8$ to both sides of the equation to isolate the term with $x$ . $\newline$ $7x - 8 + 8 = 0 + 8$ $\newline$ $7x = 8$
Divide to Find x: Divide both sides of the equation by $7$ to solve for x. $\newline$ $\frac{7x}{7} = \frac{8}{7}$ $\newline$ $x = \frac{8}{7}$

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