Algebra Examples

$3^{4 x + 5} = 81^{- \frac{3}{4}}$

Step 1

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

$3^{4 x + 5} = 3^{4 (- \frac{3}{4})}$

Step 2

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

$4 x + 5 = 4 (- \frac{3}{4})$

Step 3

Solve for $x$ .

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Step 3.1

Simplify $4 (- \frac{3}{4})$ .

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Step 3.1.1

Rewrite.

$4 x + 5 = 0 + 0 + 4 (- \frac{3}{4})$

Step 3.1.2

Simplify by adding zeros.

$4 x + 5 = 4 (- \frac{3}{4})$

Step 3.1.3

Cancel the common factor of $4$ .

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Step 3.1.3.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$4 x + 5 = 4 (\frac{- 3}{4})$

Step 3.1.3.2

Cancel the common factor.

$4 x + 5 = 4 (\frac{- 3}{4})$

Step 3.1.3.3

Rewrite the expression.

$4 x + 5 = - 3$

Step 3.2

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

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Step 3.2.1

Subtract $5$ from both sides of the equation.

$4 x = - 3 - 5$

Step 3.2.2

Subtract $5$ from $- 3$ .

$4 x = - 8$

Step 3.3

Divide each term in $4 x = - 8$ by $4$ and simplify.

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Step 3.3.1

Divide each term in $4 x = - 8$ by $4$ .

$\frac{4 x}{4} = \frac{- 8}{4}$

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.

$\frac{4 x}{4} = \frac{- 8}{4}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{4}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 8$ by $4$ .

$x = - 2$