Finite Math Examples

$e^{32} = e^{12 x}$

Step 1

Rewrite the equation as $e^{12 x} = e^{32}$ .

$e^{12 x} = e^{32}$

Step 2

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

$12 x = 32$

Step 3

Divide each term in $12 x = 32$ by $12$ and simplify.

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Step 3.1

Divide each term in $12 x = 32$ by $12$ .

$\frac{12 x}{12} = \frac{32}{12}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $12$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{32}{12}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{32}{12}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $32$ and $12$ .

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Step 3.3.1.1

Factor $4$ out of $32$ .

$x = \frac{4 (8)}{12}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $4$ out of $12$ .

$x = \frac{4 \cdot 8}{4 \cdot 3}$

Step 3.3.1.2.2

Cancel the common factor.

$x = \frac{4 \cdot 8}{4 \cdot 3}$

Step 3.3.1.2.3

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 2.\overline{6}$

Mixed Number Form:

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