Precalculus Examples

$81 = 3^{5 x + 14}$

Step 1

Rewrite the equation as $3^{5 x + 14} = 81$ .

$3^{5 x + 14} = 81$

Step 2

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

$3^{5 x + 14} = 3^{4}$

Step 3

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

$5 x + 14 = 4$

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

Subtract $14$ from both sides of the equation.

$5 x = 4 - 14$

Step 4.1.2

Subtract $14$ from $4$ .

$5 x = - 10$

Step 4.2

Divide each term in $5 x = - 10$ by $5$ and simplify.

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Step 4.2.1

Divide each term in $5 x = - 10$ by $5$ .

$\frac{5 x}{5} = \frac{- 10}{5}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $5$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 10}{5}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 10}{5}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 10$ by $5$ .

$x = - 2$