Algebra Examples

$64^{3 x} = 16^{x + 1}$

Step 1

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

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

Step 2

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

$3 (3 x) = 2 (x + 1)$

Step 3

Solve for $x$ .

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Step 3.1

Multiply $3$ by $3$ .

$9 x = 2 (x + 1)$

Step 3.2

Simplify $2 (x + 1)$ .

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Step 3.2.1

Apply the distributive property.

$9 x = 2 x + 2 \cdot 1$

Step 3.2.2

Multiply $2$ by $1$ .

$9 x = 2 x + 2$

Step 3.3

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

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Step 3.3.1

Subtract $2 x$ from both sides of the equation.

$9 x - 2 x = 2$

Step 3.3.2

Subtract $2 x$ from $9 x$ .

$7 x = 2$

Step 3.4

Divide each term in $7 x = 2$ by $7$ and simplify.

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Step 3.4.1

Divide each term in $7 x = 2$ by $7$ .

$\frac{7 x}{7} = \frac{2}{7}$

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.

$\frac{7 x}{7} = \frac{2}{7}$

Step 3.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{7}$

Decimal Form:

$x = 0.\overline{285714}$