Question

to solve (49^{3x} = 343^{2x+1}), write each side of the equation in terms of base .

Explanation:

⚡ Using what you learned: Solving Exponential Equations

Step 1: Identify the bases

The bases on both sides of the equation are \( 49 \) and \( 343 \).

Step 2: Find a common base

Express both numbers as powers of a smaller prime number:

$$ 49 = 7^2 $$

$$ 343 = 7^3 $$

Both sides can be written in terms of base \( 7 \).

Answer:

7