Algebra Examples

$\log_{5} (2) + \log_{5} (10) - \log_{5} (4)$

Step 1

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

$\log_{5} (2 \cdot 10) - \log_{5} (4)$

Step 2

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

$\log_{5} (\frac{2 \cdot 10}{4})$

Step 3

Cancel the common factor of $2$ and $4$ .

Tap for more steps...

Step 3.1

Factor $2$ out of $2 \cdot 10$ .

$\log_{5} (\frac{2 (10)}{4})$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $2$ out of $4$ .

$\log_{5} (\frac{2 \cdot 10}{2 \cdot 2})$

Step 3.2.2

Cancel the common factor.

$\log_{5} (\frac{2 \cdot 10}{2 \cdot 2})$

Step 3.2.3

Rewrite the expression.

$\log_{5} (\frac{10}{2})$

Step 4

Cancel the common factor of $10$ and $2$ .

Tap for more steps...

Step 4.1

Factor $2$ out of $10$ .

$\log_{5} (\frac{2 \cdot 5}{2})$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $2$ out of $2$ .

$\log_{5} (\frac{2 \cdot 5}{2 (1)})$

Step 4.2.2

Cancel the common factor.

$\log_{5} (\frac{2 \cdot 5}{2 \cdot 1})$

Step 4.2.3

Rewrite the expression.

$\log_{5} (\frac{5}{1})$

Step 4.2.4

Divide $5$ by $1$ .

$\log_{5} (5)$

Step 5

Logarithm base $5$ of $5$ is $1$ .

$1$