Trigonometry Examples

$\frac{1}{9} = 9^{4 x - 3}$

Step 1

Rewrite the equation as $9^{4 x - 3} = \frac{1}{9}$ .

$9^{4 x - 3} = \frac{1}{9}$

Step 2

Raise $9$ to the power of $1$ .

$9^{4 x - 3} = \frac{1}{9^{1}}$

Step 3

Move $9^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$9^{4 x - 3} = 9^{- 1}$

Step 4

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

$4 x - 3 = - 1$

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

Add $3$ to both sides of the equation.

$4 x = - 1 + 3$

Step 5.1.2

Add $- 1$ and $3$ .

$4 x = 2$

Step 5.2

Divide each term in $4 x = 2$ by $4$ and simplify.

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Step 5.2.1

Divide each term in $4 x = 2$ by $4$ .

$\frac{4 x}{4} = \frac{2}{4}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $4$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{2}{4}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{4}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Cancel the common factor of $2$ and $4$ .

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Step 5.2.3.1.1

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{4}$

Step 5.2.3.1.2

Cancel the common factors.

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Step 5.2.3.1.2.1

Factor $2$ out of $4$ .

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

Step 5.2.3.1.2.2

Cancel the common factor.

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

Step 5.2.3.1.2.3

Rewrite the expression.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.5$