Algebra Examples

$\log (6) - \log (3) + 2 \log (7)$

Step 1

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

$\log (\frac{6}{3}) + 2 \log (7)$

Step 2

Simplify each term.

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Step 2.1

Divide $6$ by $3$ .

$\log (2) + 2 \log (7)$

Step 2.2

Simplify $2 \log (7)$ by moving $2$ inside the logarithm.

$\log (2) + \log (7^{2})$

Step 2.3

Raise $7$ to the power of $2$ .

$\log (2) + \log (49)$

Step 3

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

$\log (2 \cdot 49)$

Step 4

Multiply $2$ by $49$ .

$\log (98)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (98)$

Decimal Form:

$1.99122607 \dots$