Algebra Examples

$1 - 3 \ln (x) + 4 \ln (y) + \frac{1}{2} \ln (z)$

Step 1

Simplify each term.

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Step 1.1

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

$1 - \ln (x^{3}) + 4 \ln (y) + \frac{1}{2} \cdot \ln (z)$

Step 1.2

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

$1 - \ln (x^{3}) + \ln (y^{4}) + \frac{1}{2} \cdot \ln (z)$

Step 1.3

Simplify $\frac{1}{2} \ln (z)$ by moving $\frac{1}{2}$ inside the logarithm.

$1 - \ln (x^{3}) + \ln (y^{4}) + \ln (z^{\frac{1}{2}})$

Step 2

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

$1 - \ln (x^{3}) + \ln (y^{4} z^{\frac{1}{2}})$