Algebra Examples

$5 \log (x) + \log (20) - \log (10)$

Step 1

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

$5 \log (x) + \log (\frac{20}{10})$

Step 2

Simplify each term.

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Step 2.1

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

$\log (x^{5}) + \log (\frac{20}{10})$

Step 2.2

Divide $20$ by $10$ .

$\log (x^{5}) + \log (2)$

Step 3

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

$\log (x^{5} \cdot 2)$

Step 4

Move $2$ to the left of $x^{5}$ .

$\log (2 x^{5})$