Question

solve: \\(4^{3x} = 4^2\\)

\\(\bigcirc\\) \\(x = -\frac{3}{2}\\)

\\(\bigcirc\\) \\(x = -\frac{2}{3}\\)

\\(\bigcirc\\) \\(x = \frac{2}{3}\\)

\\(\bigcirc\\) \\(x = \frac{3}{2}\\)

Explanation:

🆕 New Concept Discovered: Solving Exponential Equations with Like Bases
Set exponents equal when bases match.

Step 1: Equate the exponents

Since the bases on both sides of the equation are the same, we can set their exponents equal to each other:

$$ 4^{3x} = 4^{2} \implies 3x = 2 $$

Step 2: Solve for x

Divide both sides by \(3\) to isolate \(x\):

$$ x = \frac{2}{3} $$

Answer:

$$ x = \frac{2}{3} $$