Finite Math Examples

$4^{9 x - 5} = 16$

Step 1

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

$4^{9 x - 5} = 4^{2}$

Step 2

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

$9 x - 5 = 2$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Add $5$ to both sides of the equation.

$9 x = 2 + 5$

Step 3.1.2

Add $2$ and $5$ .

$9 x = 7$

Step 3.2

Divide each term in $9 x = 7$ by $9$ and simplify.

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Step 3.2.1

Divide each term in $9 x = 7$ by $9$ .

$\frac{9 x}{9} = \frac{7}{9}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $9$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{7}{9}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{9}$

Decimal Form:

$x = 0.\overline{7}$