Precalculus Examples

$3^{x - 1} = \frac{1}{81}$

Step 1

Raise $81$ to the power of $1$ .

$3^{x - 1} = \frac{1}{81^{1}}$

Step 2

Move $81^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3^{x - 1} = 81^{- 1}$

Step 3

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

$3^{x - 1} = 3^{- 4}$

Step 4

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

$x - 1 = - 4$

Step 5

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

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Step 5.1

Add $1$ to both sides of the equation.

$x = - 4 + 1$

Step 5.2

Add $- 4$ and $1$ .

$x = - 3$