Question

question 24 (mandatory) (1 point) if 3^{2x - 3}=27, then x is equal to a) 4 b) 2 c) 6 d) 3

Explanation:

Step1: Rewrite 27 as a power of 3

Since \(27 = 3^3\), the equation \(3^{2x - 3}=27\) becomes \(3^{2x - 3}=3^3\).

Step2: Set exponents equal

If \(a^m=a^n\), then \(m = n\). So, \(2x-3 = 3\).

Step3: Solve for x

Add 3 to both sides: \(2x-3 + 3=3 + 3\), which gives \(2x=6\). Then divide both sides by 2: \(\frac{2x}{2}=\frac{6}{2}\), so \(x = 3\).

Answer:

D. 3