Precalculus Examples

$\ln ({(1)}^{2} x) + 3 \ln (x) - 10$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

One to any power is one.

$\ln (1 x) + 3 \ln (x) - 10$

Step 1.2

Multiply $x$ by $1$ .

$\ln (x) + 3 \ln (x) - 10$

Step 1.3

Simplify $3 \ln (x)$ by moving $3$ inside the logarithm.

$\ln (x) + \ln (x^{3}) - 10$

Step 2

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

$\ln (x \cdot x^{3}) - 10$

Step 3

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

Tap for more steps...

Step 3.1

Multiply $x$ by $x^{3}$ .

Tap for more steps...

Step 3.1.1

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

$\ln (x^{1} x^{3}) - 10$

Step 3.1.2

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

$\ln (x^{1 + 3}) - 10$

Step 3.2

Add $1$ and $3$ .

$\ln (x^{4}) - 10$