Pre-Algebra Examples

$2^{x + 14} = 16^{2 x}$

Step 1

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

$2^{x + 14} = 2^{4 (2 x)}$

Step 2

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

$x + 14 = 4 (2 x)$

Step 3

Solve for $x$ .

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Step 3.1

Multiply $2$ by $4$ .

$x + 14 = 8 x$

Step 3.2

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

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Step 3.2.1

Subtract $8 x$ from both sides of the equation.

$x + 14 - 8 x = 0$

Step 3.2.2

Subtract $8 x$ from $x$ .

$- 7 x + 14 = 0$

Step 3.3

Subtract $14$ from both sides of the equation.

$- 7 x = - 14$

Step 3.4

Divide each term in $- 7 x = - 14$ by $- 7$ and simplify.

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Step 3.4.1

Divide each term in $- 7 x = - 14$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 14}{- 7}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $- 7$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 14}{- 7}$

Step 3.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 14}{- 7}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $- 14$ by $- 7$ .

$x = 2$