Precalculus Examples

$\log (4) \cdot 20 - \log (4) \cdot 5$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Multiply $\log (4) \cdot 20$ .

Tap for more steps...

Step 1.1.1

Reorder $\log (4)$ and $20$ .

$20 \cdot \log (4) - \log (4) \cdot 5$

Step 1.1.2

Simplify $20 \cdot \log (4)$ by moving $20$ inside the logarithm.

$\log (4^{20}) - \log (4) \cdot 5$

Step 1.2

Raise $4$ to the power of $20$ .

$\log (1099511627776) - \log (4) \cdot 5$

Step 1.3

Multiply $- \log (4) \cdot 5$ .

Tap for more steps...

Step 1.3.1

Multiply $5$ by $- 1$ .

$\log (1099511627776) - 5 \log (4)$

Step 1.3.2

Simplify $- 5 \log (4)$ by moving $5$ inside the logarithm.

$\log (1099511627776) - \log (4^{5})$

Step 1.4

Raise $4$ to the power of $5$ .

$\log (1099511627776) - \log (1024)$

Step 2

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

$\log (\frac{1099511627776}{1024})$

Step 3

Divide $1099511627776$ by $1024$ .

$\log (1073741824)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (1073741824)$

Decimal Form:

$9.03089986 \dots$