Write as a Single Logarithm log of 20+ log of 15-2 log of 5

$\log (20) + \log (15) - 2 \log (5)$

Step 1

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

$\log (20 \cdot 15) - 2 \log (5)$

Step 2

Simplify each term.

Multiply $20$ by $15$ .

$\log (300) - 2 \log (5)$

Simplify $- 2 \log (5)$ by moving $2$ inside the logarithm.

$\log (300) - \log (5^{2})$

Raise $5$ to the power of $2$ .

$\log (300) - \log (25)$

Step 3

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

$\log (\frac{300}{25})$

Step 4

Divide $300$ by $25$ .

$\log (12)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (12)$

Decimal Form:

$1.07918124 \dots$