Finite Math Examples

$3^{x + 3} = \frac{1}{27^{3 x}}$

Step 1

Move $27^{3 x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

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

$3^{x + 3} = 3^{3 (- 3 x)}$

Step 3

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

$x + 3 = 3 (- 3 x)$

Step 4

Solve for $x$ .

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Step 4.1

Multiply $- 3$ by $3$ .

$x + 3 = - 9 x$

Step 4.2

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

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Step 4.2.1

Add $9 x$ to both sides of the equation.

$x + 3 + 9 x = 0$

Step 4.2.2

Add $x$ and $9 x$ .

$10 x + 3 = 0$

Step 4.3

Subtract $3$ from both sides of the equation.

$10 x = - 3$

Step 4.4

Divide each term in $10 x = - 3$ by $10$ and simplify.

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Step 4.4.1

Divide each term in $10 x = - 3$ by $10$ .

$\frac{10 x}{10} = \frac{- 3}{10}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $10$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{10 x}{10} = \frac{- 3}{10}$

Step 4.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3}{10}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Move the negative in front of the fraction.

$x = - \frac{3}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{10}$

Decimal Form:

$x = - 0.3$