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Solve the exponential equation for
x.

26^(9x+5)=1

x=

Solve the exponential equation for $x$ . $\newline$ $26^{9 x+5}=1$ $\newline$ $x=$

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Solve exponential equations by rewriting the base

Full solution

Q. Solve the exponential equation for

x

.

\newline

26^{9 x+5}=1

\newline

x=

Write $1$ as Power Term: Write $1$ as a power term with $26$ as the base. $\newline$ Any natural number raised to the power of $0$ is $1$ . $\newline$ So, $1 = 26^0$
Set Exponent Equal to $0$ : Set the exponent of $26$ in the equation equal to $0$ . Since $26^{9x+5} = 26^0$ , we can equate the exponents because the bases are the same. $9x + 5 = 0$
Solve for x: Solve for x. $\newline$ Subtract $5$ from both sides of the equation. $\newline$ $9x + 5 - 5 = 0 - 5$ $\newline$ $9x = -5$
Divide to Isolate $x$ : Divide both sides by $9$ to isolate $x$ . $x = \frac{-5}{9}$

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