Question

solve: \\(6^{2x - 3} = 6^{-2x + 1}\\)

\\(\bigcirc\\) \\(x = -1\\)

\\(\bigcirc\\) \\(x = 0\\)

\\(\bigcirc\\) \\(x = 1\\)

\\(\bigcirc\\) \\(x = 4\\)

Explanation:

⚡ Using what you learned: Solving Exponential Equations

Step 1: Equate the exponents

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

$$ 2x - 3 = -2x + 1 $$

Step 2: Solve for \( x \)

Add \( 2x \) to both sides:

$$ 4x - 3 = 1 $$

Add \( 3 \) to both sides:

$$ 4x = 4 $$

Divide by \( 4 \):

$$ x = 1 $$

Answer:

\( x = 1 \)