Question

solve. write your answer as an integer or a fraction in simplest form. 81 = 9^(2x + 1) x =

Explanation:

Step1: Express 81 as a power of 9

Since \( 9^2 = 81 \), we can rewrite the equation \( 81 = 9^{2x + 1} \) as \( 9^2 = 9^{2x + 1} \).

Step2: Set the exponents equal

For exponential equations with the same base, if \( a^m = a^n \), then \( m = n \). Here, the base \( a = 9 \), so we set the exponents equal: \( 2 = 2x + 1 \).

Step3: Solve for x

Subtract 1 from both sides: \( 2 - 1 = 2x \), which simplifies to \( 1 = 2x \). Then divide both sides by 2: \( x = \frac{1}{2} \).

Answer:

\( \frac{1}{2} \)