Evaluate 49^(3x)=343^(2x+1)

$49^{3 x} = 343^{2 x + 1}$

Step 1

Create equivalent expressions in the equation that all have equal bases.

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

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 (3 x) = 3 (2 x + 1)$

Step 3

Solve for $x$ .

Multiply $3$ by $2$ .

$6 x = 3 (2 x + 1)$

Simplify $3 (2 x + 1)$ .

Apply the distributive property.

$6 x = 3 (2 x) + 3 \cdot 1$

Multiply.

Multiply $2$ by $3$ .

$6 x = 6 x + 3 \cdot 1$

Multiply $3$ by $1$ .

$6 x = 6 x + 3$

Move all terms containing $x$ to the left side of the equation.

Subtract $6 x$ from both sides of the equation.

$6 x - 6 x = 3$

Subtract $6 x$ from $6 x$ .

$0 = 3$

Since $0 \neq 3$ , there are no solutions.

No solution