Question

question 19 (mandatory) (1 point) if 3^{2x - 3}=27, then x is equal to a) 6 b) 3 c) 4 d) 2

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: Equate the exponents

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

Step3: Solve for x

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

Answer:

b) 3