Precalculus Examples

$3^{4 - x} = 27^{x}$

Step 1

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

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

Step 2

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

$4 - x = 3 x$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $3 x$ from both sides of the equation.

$4 - x - 3 x = 0$

Step 3.1.2

Subtract $3 x$ from $- x$ .

$4 - 4 x = 0$

Step 3.2

Subtract $4$ from both sides of the equation.

$- 4 x = - 4$

Step 3.3

Divide each term in $- 4 x = - 4$ by $- 4$ and simplify.

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Step 3.3.1

Divide each term in $- 4 x = - 4$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 4}{- 4}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 4$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 4}{- 4}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{- 4}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 4$ by $- 4$ .

$x = 1$