Precalculus Examples

$\ln (x) - 2 \ln (x^{2} + 1) + 0.5 \ln (3 - x^{4})$

Step 1

Simplify each term.

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Step 1.1

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

$\ln (x) - \ln ({(x^{2} + 1)}^{2}) + 0.5 \ln (3 - x^{4})$

Step 1.2

Simplify $0.5 \ln (3 - x^{4})$ by moving $0.5$ inside the logarithm.

$\ln (x) - \ln ({(x^{2} + 1)}^{2}) + \ln ({(3 - x^{4})}^{0.5})$

Step 2

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

$\ln (\frac{x}{{(x^{2} + 1)}^{2}}) + \ln ({(3 - x^{4})}^{0.5})$

Step 3

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

$\ln (\frac{x}{{(x^{2} + 1)}^{2}} {(3 - x^{4})}^{0.5})$

Step 4

Combine $\frac{x}{{(x^{2} + 1)}^{2}}$ and ${(3 - x^{4})}^{0.5}$ .

$\ln (\frac{x {(3 - x^{4})}^{0.5}}{{(x^{2} + 1)}^{2}})$