Precalculus Examples

$\log_{3} (x^{6}) + \log_{3} (18 x^{3}) - \log_{3} (18)$

Step 1

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

$\log_{3} (x^{6} (18 x^{3})) - \log_{3} (18)$

Step 2

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

$\log_{3} (\frac{x^{6} (18 x^{3})}{18})$

Step 3

Multiply $x^{6}$ by $x^{3}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $x^{3}$ .

$\log_{3} (\frac{x^{3} x^{6} \cdot 18}{18})$

Step 3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\log_{3} (\frac{x^{3 + 6} \cdot 18}{18})$

Step 3.3

Add $3$ and $6$ .

$\log_{3} (\frac{x^{9} \cdot 18}{18})$

Step 4

Cancel the common factor of $18$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

$\log_{3} (\frac{x^{9} \cdot 18}{18})$

Step 4.2

Divide $x^{9}$ by $1$ .

$\log_{3} (x^{9})$