Question

solve 3^(3x - 6) = 27 what is the solution set

Explanation:

Step1: Rewrite 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 (since bases are same)

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

Step3: Solve for x

Add 6 to both sides: \(3x-6 + 6=3 + 6\), which simplifies to \(3x=9\). Then divide both sides by 3: \(\frac{3x}{3}=\frac{9}{3}\), so \(x = 3\).

Answer:

The solution set is \(\{3\}\)