Finite Math Examples

$3^{7 - 2 x} = 3^{3 x - 5}$

Step 1

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

$3^{7 - 2 x} = 3^{3 x - 5}$

Step 2

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

$7 - 2 x = 3 x - 5$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $3 x$ from both sides of the equation.

$7 - 2 x - 3 x = - 5$

Step 3.1.2

Subtract $3 x$ from $- 2 x$ .

$7 - 5 x = - 5$

Step 3.2

Move all terms not containing $x$ to the right side of the equation.

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Step 3.2.1

Subtract $7$ from both sides of the equation.

$- 5 x = - 5 - 7$

Step 3.2.2

Subtract $7$ from $- 5$ .

$- 5 x = - 12$

Step 3.3

Divide each term in $- 5 x = - 12$ by $- 5$ and simplify.

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Step 3.3.1

Divide each term in $- 5 x = - 12$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 12}{- 5}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 5$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 12}{- 5}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{- 5}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{12}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{12}{5}$

Decimal Form:

$x = 2.4$

Mixed Number Form:

$x = 2 \frac{2}{5}$