Calculus Examples

$\frac{1}{3^{4 x}} = 3^{10 x - 6}$

Step 1

Move $3^{4 x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$3^{- 4 x} = 3^{10 x - 6}$

Step 2

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

$- 4 x = 10 x - 6$

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 $10 x$ from both sides of the equation.

$- 4 x - 10 x = - 6$

Step 3.1.2

Subtract $10 x$ from $- 4 x$ .

$- 14 x = - 6$

Step 3.2

Divide each term in $- 14 x = - 6$ by $- 14$ and simplify.

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Step 3.2.1

Divide each term in $- 14 x = - 6$ by $- 14$ .

$\frac{- 14 x}{- 14} = \frac{- 6}{- 14}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 14$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 14 x}{- 14} = \frac{- 6}{- 14}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 6}{- 14}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Cancel the common factor of $- 6$ and $- 14$ .

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Step 3.2.3.1.1

Factor $- 2$ out of $- 6$ .

$x = \frac{- 2 (3)}{- 14}$

Step 3.2.3.1.2

Cancel the common factors.

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Step 3.2.3.1.2.1

Factor $- 2$ out of $- 14$ .

$x = \frac{- 2 \cdot 3}{- 2 \cdot 7}$

Step 3.2.3.1.2.2

Cancel the common factor.

$x = \frac{- 2 \cdot 3}{- 2 \cdot 7}$

Step 3.2.3.1.2.3

Rewrite the expression.

$x = \frac{3}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{7}$

Decimal Form:

$x = 0.\overline{428571}$