Precalculus Examples

$\log_{6} (8) + \log_{6} (5) - 2 \log_{6} (2)$

Step 1

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

$\log_{6} (8 \cdot 5) - 2 \log_{6} (2)$

Step 2

Simplify each term.

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Step 2.1

Multiply $8$ by $5$ .

$\log_{6} (40) - 2 \log_{6} (2)$

Step 2.2

Simplify $- 2 \log_{6} (2)$ by moving $2$ inside the logarithm.

$\log_{6} (40) - \log_{6} (2^{2})$

Step 2.3

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

$\log_{6} (40) - \log_{6} (4)$

Step 3

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

$\log_{6} (\frac{40}{4})$

Step 4

Divide $40$ by $4$ .

$\log_{6} (10)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log_{6} (10)$

Decimal Form:

$1.28509720 \dots$