Question

solve 3^(3x - 6) = 27

Explanation:

Step1: Express 27 as a power of 3

Since \( 27 = 3^3 \), the equation \( 3^{(3x - 6)} = 27 \) can be rewritten as \( 3^{(3x - 6)} = 3^3 \).

Step2: Set exponents equal

For exponential equations with the same base (\( a^m = a^n \) implies \( m = n \) when \( a>0,a
eq1 \)), we have \( 3x - 6 = 3 \).

Step3: Solve for x

Add 6 to both sides: \( 3x = 3 + 6 \), so \( 3x = 9 \). Divide both sides by 3: \( x = \frac{9}{3} = 3 \).

Answer:

\( x = 3 \)