Precalculus Examples

$2^{3 x - 1} = \frac{1}{2}$

Step 1

Raise $2$ to the power of $1$ .

$2^{3 x - 1} = \frac{1}{2^{1}}$

Step 2

Move $2^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$2^{3 x - 1} = 2^{- 1}$

Step 3

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

$3 x - 1 = - 1$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Add $1$ to both sides of the equation.

$3 x = - 1 + 1$

Step 4.1.2

Add $- 1$ and $1$ .

$3 x = 0$

Step 4.2

Divide each term in $3 x = 0$ by $3$ and simplify.

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Step 4.2.1

Divide each term in $3 x = 0$ by $3$ .

$\frac{3 x}{3} = \frac{0}{3}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $3$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{0}{3}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{3}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $0$ by $3$ .

$x = 0$