Finite Math Examples

$4 {(2)}^{3 x} = 1024$

Step 1

Rewrite $4$ as $2^{2}$ .

$2^{2} \cdot 2^{3 x} = 1024$

Step 2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{2 + 3 x} = 1024$

Step 3

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

$2^{2 + 3 x} = 2^{10}$

Step 4

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

$2 + 3 x = 10$

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 $2$ from both sides of the equation.

$3 x = 10 - 2$

Step 5.1.2

Subtract $2$ from $10$ .

$3 x = 8$

Step 5.2

Divide each term in $3 x = 8$ by $3$ and simplify.

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Step 5.2.1

Divide each term in $3 x = 8$ by $3$ .

$\frac{3 x}{3} = \frac{8}{3}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $3$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{8}{3}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{8}{3}$

Decimal Form:

$x = 2.\overline{6}$

Mixed Number Form:

$x = 2 \frac{2}{3}$