Finite Math Examples

$3^{- 5 x} = 27$

Step 1

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

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

Step 2

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

$- 5 x = 3$

Step 3

Divide each term in $- 5 x = 3$ by $- 5$ and simplify.

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Step 3.1

Divide each term in $- 5 x = 3$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{3}{- 5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{3}{- 5}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{- 5}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$x = - \frac{3}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{5}$

Decimal Form:

$x = - 0.6$