Precalculus Examples

$2 \cdot 5^{\frac{x}{4}} = 250$

Step 1

Divide each term in $2 \cdot 5^{\frac{x}{4}} = 250$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 \cdot 5^{\frac{x}{4}} = 250$ by $2$ .

$\frac{2 \cdot 5^{\frac{x}{4}}}{2} = \frac{250}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 \cdot 5^{\frac{x}{4}}}{2} = \frac{250}{2}$

Step 1.2.1.2

Divide $5^{\frac{x}{4}}$ by $1$ .

$5^{\frac{x}{4}} = \frac{250}{2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $250$ by $2$ .

$5^{\frac{x}{4}} = 125$

Step 2

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

$5^{\frac{x}{4}} = 5^{3}$

Step 3

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

$\frac{x}{4} = 3$

Step 4

Solve for $x$ .

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Step 4.1

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 \cdot 3$

Step 4.2

Simplify both sides of the equation.

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Cancel the common factor of $4$ .

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Step 4.2.1.1.1

Cancel the common factor.

$4 \frac{x}{4} = 4 \cdot 3$

Step 4.2.1.1.2

Rewrite the expression.

$x = 4 \cdot 3$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Multiply $4$ by $3$ .

$x = 12$