Precalculus Examples

$\log (5) \cdot 10 - \log (5 m)$

Step 1

Simplify each term.

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Step 1.1

Multiply $\log (5) \cdot 10$ .

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Step 1.1.1

Reorder $\log (5)$ and $10$ .

$10 \cdot \log (5) - \log (5 m)$

Step 1.1.2

Simplify $10 \cdot \log (5)$ by moving $10$ inside the logarithm.

$\log (5^{10}) - \log (5 m)$

Step 1.2

Raise $5$ to the power of $10$ .

$\log (9765625) - \log (5 m)$

Step 2

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

$\log (\frac{9765625}{5 m})$

Step 3

Cancel the common factor of $9765625$ and $5$ .

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Step 3.1

Factor $5$ out of $9765625$ .

$\log (\frac{5 \cdot 1953125}{5 m})$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $5$ out of $5 m$ .

$\log (\frac{5 \cdot 1953125}{5 (m)})$

Step 3.2.2

Cancel the common factor.

$\log (\frac{5 \cdot 1953125}{5 m})$

Step 3.2.3

Rewrite the expression.

$\log (\frac{1953125}{m})$