Algebra Examples

$8^{y} = 16^{y + 2}$

Step 1

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

$2^{3 y} = 2^{4 (y + 2)}$

Step 2

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

$3 y = 4 (y + 2)$

Step 3

Solve for $y$ .

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Step 3.1

Simplify $4 (y + 2)$ .

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Step 3.1.1

Apply the distributive property.

$3 y = 4 y + 4 \cdot 2$

Step 3.1.2

Multiply $4$ by $2$ .

$3 y = 4 y + 8$

Step 3.2

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

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Step 3.2.1

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

$3 y - 4 y = 8$

Step 3.2.2

Subtract $4 y$ from $3 y$ .

$- y = 8$

Step 3.3

Divide each term in $- y = 8$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- y = 8$ by $- 1$ .

$\frac{- y}{- 1} = \frac{8}{- 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{8}{- 1}$

Step 3.3.2.2

Divide $y$ by $1$ .

$y = \frac{8}{- 1}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $8$ by $- 1$ .

$y = - 8$