Precalculus Examples

$4 \ln (x^{\frac{3}{3}}) + \ln (3 x)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Divide $3$ by $3$ .

$4 \ln (x^{1}) + \ln (3 x)$

Step 1.2

Simplify.

$4 \ln (x) + \ln (3 x)$

Step 1.3

Simplify $4 \ln (x)$ by moving $4$ inside the logarithm.

$\ln (x^{4}) + \ln (3 x)$

Step 2

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

$\ln (x^{4} (3 x))$

Step 3

Rewrite using the commutative property of multiplication.

$\ln (3 x^{4} x)$

Step 4

Multiply $x^{4}$ by $x$ by adding the exponents.

Tap for more steps...

Step 4.1

Move $x$ .

$\ln (3 (x \cdot x^{4}))$

Step 4.2

Multiply $x$ by $x^{4}$ .

Tap for more steps...

Step 4.2.1

Raise $x$ to the power of $1$ .

$\ln (3 (x^{1} x^{4}))$

Step 4.2.2

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

$\ln (3 x^{1 + 4})$

Step 4.3

Add $1$ and $4$ .

$\ln (3 x^{5})$