Precalculus Examples

$\log (4) - \log (8) + \log (3) + \log (5)$

Step 1

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

$\log (\frac{4}{8}) + \log (3) + \log (5)$

Step 2

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

$\log (\frac{4}{8} \cdot 3) + \log (5)$

Step 3

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

$\log (\frac{4}{8} \cdot 3 \cdot 5)$

Step 4

Cancel the common factor of $4$ and $8$ .

Tap for more steps...

Step 4.1

Factor $4$ out of $4$ .

$\log (\frac{4 (1)}{8} \cdot 3 \cdot 5)$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $4$ out of $8$ .

$\log (\frac{4 \cdot 1}{4 \cdot 2} \cdot 3 \cdot 5)$

Step 4.2.2

Cancel the common factor.

$\log (\frac{4 \cdot 1}{4 \cdot 2} \cdot 3 \cdot 5)$

Step 4.2.3

Rewrite the expression.

$\log (\frac{1}{2} \cdot 3 \cdot 5)$

Step 5

Combine $\frac{1}{2}$ and $3$ .

$\log (\frac{3}{2} \cdot 5)$

Step 6

Multiply $\frac{3}{2} \cdot 5$ .

Tap for more steps...

Step 6.1

Combine $\frac{3}{2}$ and $5$ .

$\log (\frac{3 \cdot 5}{2})$

Step 6.2

Multiply $3$ by $5$ .

$\log (\frac{15}{2})$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\log (\frac{15}{2})$

Decimal Form:

$0.87506126 \dots$