Solve for k 8^(3k+4)=4^(2k-1)

$8^{3 k + 4} = 4^{2 k - 1}$

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

$2^{3 (3 k + 4)} = 2^{2 (2 k - 1)}$

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

$3 (3 k + 4) = 2 (2 k - 1)$

Solve for $k$ .

Simplify $3 (3 k + 4)$ .

Start simplifying.

$0 + 0 + 3 (3 k + 4) = 2 (2 k - 1)$

Simplify by adding zeros.

$3 (3 k + 4) = 2 (2 k - 1)$

Apply the distributive property.

$3 (3 k) + 3 \cdot 4 = 2 (2 k - 1)$

Multiply.

Multiply $3$ by $3$ .

$9 k + 3 \cdot 4 = 2 (2 k - 1)$

Multiply $3$ by $4$ .

$9 k + 12 = 2 (2 k - 1)$

Simplify $2 (2 k - 1)$ .

Apply the distributive property.

$9 k + 12 = 2 (2 k) + 2 \cdot - 1$

Multiply.

Multiply $2$ by $2$ .

$9 k + 12 = 4 k + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$9 k + 12 = 4 k - 2$

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

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

$9 k + 12 - 4 k = - 2$

Subtract $4 k$ from $9 k$ .

$5 k + 12 = - 2$

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

Subtract $12$ from both sides of the equation.

$5 k = - 2 - 12$

Subtract $12$ from $- 2$ .

$5 k = - 14$

Divide each term in $5 k = - 14$ by $5$ and simplify.

Divide each term in $5 k = - 14$ by $5$ .

$\frac{5 k}{5} = \frac{- 14}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 k}{5} = \frac{- 14}{5}$

Divide $k$ by $1$ .

$k = \frac{- 14}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$k = - \frac{14}{5}$

The result can be shown in multiple forms.

Exact Form:

$k = - \frac{14}{5}$

Decimal Form:

$k = - 2.8$

Mixed Number Form:

$k = - 2 \frac{4}{5}$

Solve for k 8^(3k+4)=4^(2k-1)

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