Precalculus Examples

4^{3 x + 2} = 4

$4^{3 x + 2} = 4$

Step 1

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

4^{3 x + 2} = 4^{1}

$4^{3 x + 2} = 4^{1}$

Step 2

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

3 x + 2 = 1

$3 x + 2 = 1$

Step 3

Solve for

x

$x$ .

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Step 3.1

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 3.1.1

Subtract

2

$2$ from both sides of the equation.

3 x = 1 - 2

$3 x = 1 - 2$

Step 3.1.2

Subtract

2

$2$ from

1

$1$ .

3 x = - 1

$3 x = - 1$

3 x = - 1

$3 x = - 1$

Step 3.2

Divide each term in

3 x = - 1

$3 x = - 1$ by

3

$3$ and simplify.

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Step 3.2.1

Divide each term in

3 x = - 1

$3 x = - 1$ by

3

$3$ .

\frac{3 x}{3} = \frac{- 1}{3}

$\frac{3 x}{3} = \frac{- 1}{3}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of

3

$3$ .

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Step 3.2.2.1.1

Cancel the common factor.

\frac{3 x}{3} = \frac{- 1}{3}

$\frac{3 x}{3} = \frac{- 1}{3}$

Step 3.2.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{- 1}{3}

$x = \frac{- 1}{3}$

x = \frac{- 1}{3}

$x = \frac{- 1}{3}$

x = \frac{- 1}{3}

$x = \frac{- 1}{3}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

x = - \frac{1}{3}

$x = - \frac{1}{3}$

x = - \frac{1}{3}

$x = - \frac{1}{3}$

x = - \frac{1}{3}

$x = - \frac{1}{3}$

x = - \frac{1}{3}

$x = - \frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

x = - \frac{1}{3}

$x = - \frac{1}{3}$

Decimal Form:

x = - 0.\overline{3}

$x = - 0.\overline{3}$

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