Finite Math Examples

$\log (5) - \log (10) = x$

Step 1

Rewrite the equation as $x = \log (5) - \log (10)$ .

$x = \log (5) - \log (10)$

Step 2

Simplify $\log (5) - \log (10)$ .

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Step 2.1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$x = \log (\frac{5}{10})$

Step 2.2

Cancel the common factor of $5$ and $10$ .

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Step 2.2.1

Factor $5$ out of $5$ .

$x = \log (\frac{5 (1)}{10})$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $5$ out of $10$ .

$x = \log (\frac{5 \cdot 1}{5 \cdot 2})$

Step 2.2.2.2

Cancel the common factor.

$x = \log (\frac{5 \cdot 1}{5 \cdot 2})$

Step 2.2.2.3

Rewrite the expression.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.30102999 \dots$