Precalculus Examples

$\log_{3} (24) + \frac{1}{2} \cdot \log_{3} (7) - \log_{3} (6)$

Step 1

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

$\frac{1}{2} \cdot \log_{3} (7) + \log_{3} (\frac{24}{6})$

Step 2

Simplify each term.

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Step 2.1

Simplify $\frac{1}{2} \log_{3} (7)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{3} (7^{\frac{1}{2}}) + \log_{3} (\frac{24}{6})$

Step 2.2

Divide $24$ by $6$ .

$\log_{3} (7^{\frac{1}{2}}) + \log_{3} (4)$

Step 3

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

$\log_{3} (7^{\frac{1}{2}} \cdot 4)$

Step 4

Move $4$ to the left of $7^{\frac{1}{2}}$ .

$\log_{3} (4 \cdot 7^{\frac{1}{2}})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log_{3} (4 \cdot 7^{\frac{1}{2}})$

Decimal Form:

$2.14748138 \dots$