Precalculus Examples

$\log (\frac{5}{2}) + \log (\frac{200000}{5})$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (\frac{5}{2} \cdot \frac{200000}{5})$

Step 2

Cancel the common factor of $5$ .

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Step 2.1

Cancel the common factor.

$\log (\frac{5}{2} \cdot \frac{200000}{5})$

Step 2.2

Rewrite the expression.

$\log (\frac{1}{2} \cdot 200000)$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $200000$ .

$\log (\frac{1}{2} \cdot (2 (100000)))$

Step 3.2

Cancel the common factor.

$\log (\frac{1}{2} \cdot (2 \cdot 100000))$

Step 3.3

Rewrite the expression.

$\log (100000)$

Step 4

Logarithm base $10$ of $100000$ is $5$ .

$5$