Finite Math Examples

$\log (5 x) - \log (65) + \log (55)$

Step 1

Rewrite $\log (5 x)$ as $\log (5) + \log (x)$ .

$\log (5) + \log (x) - \log (65) + \log (55)$

Step 2

Simplify each term.

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Rewrite $\log (65)$ as $\log (5 (13))$ .

$\log (5) + \log (x) - \log (5 (13)) + \log (55)$

Rewrite $\log (5 (13))$ as $\log (5) + \log (13)$ .

$\log (5) + \log (x) - (\log (5) + \log (13)) + \log (55)$

Apply the distributive property.

$\log (5) + \log (x) - \log (5) - \log (13) + \log (55)$

Rewrite $\log (55)$ as $\log (5 (11))$ .

$\log (5) + \log (x) - \log (5) - \log (13) + \log (5 (11))$

Rewrite $\log (5 (11))$ as $\log (5) + \log (11)$ .

$\log (5) + \log (x) - \log (5) - \log (13) + \log (5) + \log (11)$

Step 3

Subtract $\log (5)$ from $\log (5)$ .

$0 + \log (x) - \log (13) + \log (5) + \log (11)$

Step 4

Add $0$ and $\log (x)$ .

$\log (x) - \log (13) + \log (5) + \log (11)$