Finite Math Examples

$\log (25) x = \frac{1}{2}$

Step 1

Divide each term in $\log (25) x = \frac{1}{2}$ by $\log (25)$ .

$\frac{\log (25) x}{\log (25)} = \frac{\frac{1}{2}}{\log (25)}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $\log (25)$ .

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Step 2.1.1

Cancel the common factor.

$\frac{\log (25) x}{\log (25)} = \frac{\frac{1}{2}}{\log (25)}$

Step 2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{1}{2}}{\log (25)}$

Step 3

Simplify the right side.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{1}{2} \cdot \frac{1}{\log (25)}$

Step 3.2

Multiply $\frac{1}{2} \cdot \frac{1}{\log (25)}$ .

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Step 3.2.1

Multiply $\frac{1}{2}$ by $\frac{1}{\log (25)}$ .

$x = \frac{1}{2 \log (25)}$

Step 3.2.2

Simplify $2 \log (25)$ by moving $2$ inside the logarithm.

$x = \frac{1}{\log (25^{2})}$

Step 3.3

Raise $25$ to the power of $2$ .

$x = \frac{1}{\log (625)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{\log (625)}$

Decimal Form:

$x = 0.35766913 \dots$