Finite Math Examples

$2 (7^{3 x}) = 98$

Step 1

Divide each term in $2 \cdot 7^{3 x} = 98$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 \cdot 7^{3 x} = 98$ by $2$ .

$\frac{2 \cdot 7^{3 x}}{2} = \frac{98}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 \cdot 7^{3 x}}{2} = \frac{98}{2}$

Step 1.2.1.2

Divide $7^{3 x}$ by $1$ .

$7^{3 x} = \frac{98}{2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $98$ by $2$ .

$7^{3 x} = 49$

Step 2

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

$7^{3 x} = 7^{2}$

Step 3

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

$3 x = 2$

Step 4

Divide each term in $3 x = 2$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 x = 2$ by $3$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{6}$