Precalculus Examples

$3^{- 3 k} = 3^{- 3 k}$

Step 1

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

$3^{- 3 k} = 3^{- 3 k}$

Step 2

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

$- 3 k = - 3 k$

Step 3

Solve for $k$ .

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Step 3.1

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

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Step 3.1.1

Add $3 k$ to both sides of the equation.

$- 3 k + 3 k = 0$

Step 3.1.2

Add $- 3 k$ and $3 k$ .

$0 = 0$

Step 3.2

Since $0 = 0$ , the equation will always be true for any value of $k$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$