Precalculus Examples

$25^{x} - 125 = 0$

Step 1

Add $125$ to both sides of the equation.

$25^{x} = 125$

Step 2

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

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

Step 3

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

$2 x = 3$

Step 4

Divide each term in $2 x = 3$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 x = 3$ by $2$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.5$

Mixed Number Form:

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