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$Solve the exponential equation for x. {:[((9)/(8))^(3x+12)=1],[x=]:}$

Solve the exponential equation for $x$ . $\newline$ $\begin{array}{l} \left(\frac{9}{8}\right)^{3 x+12}=1 \\ x=\square \end{array}$

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Evaluate exponential functions

Full solution

Q. Solve the exponential equation for

x

.

\newline

\begin{array}{l} \left(\frac{9}{8}\right)^{3 x+12}=1 \\ x=\square \end{array}

Identify given equation: Identify the given exponential equation and the value it is equal to. $\newline$ The given equation is $\left(\frac{9}{8}\right)^{3x+12} = 1$ . We need to find the value of $x$ that satisfies this equation.
Recognize power property: Recognize that any non-zero number raised to the power of $0$ is $1$ . Since $\left(\frac{9}{8}\right)^{3x+12} = 1$ , we can deduce that the exponent $3x+12$ must be equal to $0$ because $\frac{9}{8}$ is a non-zero number.
Set exponent equal: Set the exponent equal to $0$ and solve for $x$ . $\newline$ $3x + 12 = 0$ $\newline$ Subtract $12$ from both sides of the equation to isolate the term with $x$ . $\newline$ $3x + 12 - 12 = 0 - 12$ $\newline$ $3x = -12$
Divide and solve for x: Divide both sides of the equation by $3$ to solve for x. $\newline$ $\frac{3x}{3} = \frac{-12}{3}$ $\newline$ $x = -4$

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