Finite Math Examples

$27 = 3^{- 4 + 8 x}$

Step 1

Rewrite the equation as $3^{- 4 + 8 x} = 27$ .

$3^{- 4 + 8 x} = 27$

Step 2

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

$3^{- 4 + 8 x} = 3^{3}$

Step 3

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

$- 4 + 8 x = 3$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Add $4$ to both sides of the equation.

$8 x = 3 + 4$

Step 4.1.2

Add $3$ and $4$ .

$8 x = 7$

Step 4.2

Divide each term in $8 x = 7$ by $8$ and simplify.

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Step 4.2.1

Divide each term in $8 x = 7$ by $8$ .

$\frac{8 x}{8} = \frac{7}{8}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $8$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{7}{8}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{8}$

Decimal Form:

$x = 0.875$