Precalculus Examples

$\log (3) \cdot (9 x^{4}) - \log (3) \cdot (3 x^{2})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify $9 \log (3)$ by moving $9$ inside the logarithm.

$\log (3^{9}) x^{4} - \log (3) \cdot (3 x^{2})$

Step 1.2

Raise $3$ to the power of $9$ .

$\log (19683) x^{4} - \log (3) \cdot (3 x^{2})$

Step 1.3

Multiply $- \log (3) (3 x^{2})$ .

Tap for more steps...

Step 1.3.1

Multiply $3$ by $- 1$ .

$\log (19683) x^{4} - 3 \log (3) x^{2}$

Step 1.3.2

Simplify $- 3 \log (3)$ by moving $3$ inside the logarithm.

$\log (19683) x^{4} - \log (3^{3}) x^{2}$

Step 1.4

Raise $3$ to the power of $3$ .

$\log (19683) x^{4} - \log (27) x^{2}$

Step 2

Reorder factors in $\log (19683) x^{4} - \log (27) x^{2}$ .

$x^{4} \log (19683) - x^{2} \log (27)$