Question

solve. write your answer as an integer or a fraction in simplest form. \\(49 = 7^{2x}\\) \\(x = \square\\)

Explanation:

Step1: Express 49 as a power of 7

Since \( 49 = 7^2 \), we can rewrite the equation \( 49 = 7^{2x} \) as \( 7^2 = 7^{2x} \).

Step2: Set the exponents equal

For exponential equations with the same base, if \( a^m = a^n \), then \( m = n \). Here, the base is 7, so we set the exponents equal: \( 2 = 2x \).

Step3: Solve for x

Divide both sides of the equation \( 2 = 2x \) by 2: \( x=\frac{2}{2}=1 \).

Answer:

\( x = 1 \)