Trigonometry Examples

$2^{9 - 2 x} = \frac{1}{32}$

Step 1

Raise $32$ to the power of $1$ .

$2^{9 - 2 x} = \frac{1}{32^{1}}$

Step 2

Move $32^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$2^{9 - 2 x} = 32^{- 1}$

Step 3

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

$2^{9 - 2 x} = 2^{- 5}$

Step 4

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

$9 - 2 x = - 5$

Step 5

Solve for $x$ .

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Step 5.1

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

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Step 5.1.1

Subtract $9$ from both sides of the equation.

$- 2 x = - 5 - 9$

Step 5.1.2

Subtract $9$ from $- 5$ .

$- 2 x = - 14$

Step 5.2

Divide each term in $- 2 x = - 14$ by $- 2$ and simplify.

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Step 5.2.1

Divide each term in $- 2 x = - 14$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 14}{- 2}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $- 2$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 14}{- 2}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 14}{- 2}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $- 14$ by $- 2$ .

$x = 7$