Calculus Examples

$\log_{20} (\frac{410}{1234})$

Step 1

Rewrite $\log_{20} (\frac{410}{1234})$ as $\log_{20} (410) - \log_{20} (1234)$ .

$\log_{20} (410) - \log_{20} (1234)$

Step 2

Rewrite $\log_{20} (1234)$ as $\log_{20} (2 (617))$ .

$\log_{20} (410) - \log_{20} (2 (617))$

Step 3

Rewrite $\log_{20} (2 (617))$ as $\log_{20} (2) + \log_{20} (617)$ .

$\log_{20} (410) - (\log_{20} (2) + \log_{20} (617))$

Step 4

Apply the distributive property.

$\log_{20} (410) - \log_{20} (2) - \log_{20} (617)$

Step 5

Simplify each term.

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Step 5.1

Rewrite $\log_{20} (410)$ as $\log_{20} (2 \cdot 5 \cdot 41)$ .

$\log_{20} (2 \cdot 5 \cdot 41) - \log_{20} (2) - \log_{20} (617)$

Step 5.2

Rewrite $\log_{20} (2 \cdot 5 \cdot 41)$ as $\log_{20} (2 \cdot 5) + \log_{20} (41)$ .

$\log_{20} (2 \cdot 5) + \log_{20} (41) - \log_{20} (2) - \log_{20} (617)$

Step 5.3

Rewrite $\log_{20} (2 \cdot 5)$ as $\log_{20} (2) + \log_{20} (5)$ .

$\log_{20} (2) + \log_{20} (5) + \log_{20} (41) - \log_{20} (2) - \log_{20} (617)$

Step 6

Subtract $\log_{20} (2)$ from $\log_{20} (2)$ .

$0 + \log_{20} (5) + \log_{20} (41) - \log_{20} (617)$

Step 7

Add $0$ and $\log_{20} (5)$ .

$\log_{20} (5) + \log_{20} (41) - \log_{20} (617)$