Question

solve: (49^{3x} = 343^{2x+1})

• (x = -3)
• (x = 1)
• (x = 3)
• no solution

Explanation:

⚡ Using what you learned: Solving Exponential Equations

Step 1: Rewrite with a common base

$$ 49 = 7^2 $$

$$ 343 = 7^3 $$

Substitute these bases into the equation:

$$ (7^2)^{3x} = (7^3)^{2x+1} $$

Step 2: Simplify exponents

$$ 7^{2 \cdot 3x} = 7^{3(2x+1)} $$

$$ 7^{6x} = 7^{6x+3} $$

Step 3: Solve for x

Since the bases are the same, set the exponents equal to each other:

$$ 6x = 6x + 3 $$

$$ 0 = 3 $$

Since this statement is false, there is no solution.

Answer:

no solution