Solve for x 7^(3x+4)=49^(2x+1)

$7^{3 x + 4} = 49^{2 x + 1}$

Step 1

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

$7^{3 x + 4} = 7^{2 (2 x + 1)}$

Step 2

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

$3 x + 4 = 2 (2 x + 1)$

Step 3

Solve for $x$ .

Simplify $2 (2 x + 1)$ .

Rewrite.

$3 x + 4 = 0 + 0 + 2 (2 x + 1)$

Simplify by adding zeros.

$3 x + 4 = 2 (2 x + 1)$

Apply the distributive property.

$3 x + 4 = 2 (2 x) + 2 \cdot 1$

Multiply.

Multiply $2$ by $2$ .

$3 x + 4 = 4 x + 2 \cdot 1$

Multiply $2$ by $1$ .

$3 x + 4 = 4 x + 2$

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

Subtract $4 x$ from both sides of the equation.

$3 x + 4 - 4 x = 2$

Subtract $4 x$ from $3 x$ .

$- x + 4 = 2$

Move all terms not containing $x$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$- x = 2 - 4$

Subtract $4$ from $2$ .

$- x = - 2$

Divide each term in $- x = - 2$ by $- 1$ and simplify.

Divide each term in $- x = - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x = 2$