Finite Math Examples

$5^{4} = 25^{2 x}$

Step 1

Rewrite the equation as $25^{2 x} = 5^{4}$ .

$25^{2 x} = 5^{4}$

Step 2

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

$5^{2 (2 x)} = 5^{4}$

Step 3

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

$2 (2 x) = 4$

Step 4

Solve for $x$ .

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Step 4.1

Multiply $2$ by $2$ .

$4 \cdot x = 4$

Step 4.2

Divide each term in $4 \cdot x = 4$ by $4$ and simplify.

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Step 4.2.1

Divide each term in $4 \cdot x = 4$ by $4$ .

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $4$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

Divide $x$ by $1$ .

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

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $4$ by $4$ .

$x = 1$