Finite Math Examples

$4^{4 - 3 x} = 4^{9 x - 7}$

Step 1

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

$4^{4 - 3 x} = 4^{9 x - 7}$

Step 2

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

$4 - 3 x = 9 x - 7$

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 $9 x$ from both sides of the equation.

$4 - 3 x - 9 x = - 7$

Step 3.1.2

Subtract $9 x$ from $- 3 x$ .

$4 - 12 x = - 7$

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 $4$ from both sides of the equation.

$- 12 x = - 7 - 4$

Step 3.2.2

Subtract $4$ from $- 7$ .

$- 12 x = - 11$

Step 3.3

Divide each term in $- 12 x = - 11$ by $- 12$ and simplify.

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Step 3.3.1

Divide each term in $- 12 x = - 11$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{- 11}{- 12}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 12$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{- 11}{- 12}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 11}{- 12}$

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.

$x = \frac{11}{12}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{12}$

Decimal Form:

$x = 0.91\overline{6}$