Algebra Examples

${(\frac{1}{5})}^{x} = {(\frac{1}{5})}^{3 x}$

Step 1

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

${(\frac{1}{5})}^{x} = {(\frac{1}{5})}^{3 x}$

Step 2

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

$x = 3 x$

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.

$x - 3 x = 0$

Step 3.1.2

Subtract $3 x$ from $x$ .

$- 2 x = 0$

Step 3.2

Divide each term in $- 2 x = 0$ by $- 2$ and simplify.

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Step 3.2.1

Divide each term in $- 2 x = 0$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{0}{- 2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{0}{- 2}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{- 2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $0$ by $- 2$ .

$x = 0$