Calculus Examples

$\frac{1}{2} \cdot \ln (x) + 8 \ln (y) - 3 \ln (z)$

Step 1

Simplify each term.

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Step 1.1

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

$\ln (x^{\frac{1}{2}}) + 8 \ln (y) - 3 \ln (z)$

Step 1.2

Simplify $8 \ln (y)$ by moving $8$ inside the logarithm.

$\ln (x^{\frac{1}{2}}) + \ln (y^{8}) - 3 \ln (z)$

Step 1.3

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

$\ln (x^{\frac{1}{2}}) + \ln (y^{8}) - \ln (z^{3})$

Step 2

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

$\ln (x^{\frac{1}{2}} y^{8}) - \ln (z^{3})$

Step 3

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

$\ln (\frac{x^{\frac{1}{2}} y^{8}}{z^{3}})$

Step 4

Reorder factors in $\ln (\frac{x^{\frac{1}{2}} y^{8}}{z^{3}})$ .

$\ln (\frac{y^{8} x^{\frac{1}{2}}}{z^{3}})$