Algebra Examples

$3^{- x} = 27$

Step 1

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

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

Step 2

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

$- x = 3$

Step 3

Divide each term in $- x = 3$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- x = 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{3}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{3}{- 1}$

Step 3.2.2

Divide $x$ by $1$ .

$x = \frac{3}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $3$ by $- 1$ .

$x = - 3$