Algebra Examples

25^{x} = 125

$25^{x} = 125$

Step 1

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

5^{2 x} = 5^{3}

$5^{2 x} = 5^{3}$

Step 2

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

2 x = 3

$2 x = 3$

Step 3

Divide each term in

2 x = 3

$2 x = 3$ by

2

$2$ and simplify.

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Step 3.1

Divide each term in

2 x = 3

$2 x = 3$ by

2

$2$ .

\frac{2 x}{2} = \frac{3}{2}

$\frac{2 x}{2} = \frac{3}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

2

$2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Step 3.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}$

Decimal Form:

$x = 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}$