Question

if \\(3^{2x+1} = 3^{x+5}\\), what is the value of \\(x\\)?

\\(\bigcirc\\) 2
\\(\bigcirc\\) 3
\\(\bigcirc\\) 4
\\(\bigcirc\\) 6

Explanation:

⚡ Using what you learned: Solving Exponential Equations

Step 1: Equate the exponents

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

$$ 2x + 1 = x + 5 $$

Step 2: Solve for \( x \)

Subtract \( x \) from both sides:

$$ x + 1 = 5 $$

Subtract 1 from both sides:

$$ x = 4 $$

Answer:

4