Algebra Examples

$\frac{1}{2} \log (r) + \frac{1}{3} \log (s) - \frac{1}{4} \log (t)$

Step 1

Simplify each term.

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Step 1.1

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

$\log (r^{\frac{1}{2}}) + \frac{1}{3} \cdot \log (s) - \frac{1}{4} \cdot \log (t)$

Step 1.2

Simplify $\frac{1}{3} \log (s)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log (r^{\frac{1}{2}}) + \log (s^{\frac{1}{3}}) - \frac{1}{4} \cdot \log (t)$

Step 1.3

Multiply $- \frac{1}{4} \log (t)$ .

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Step 1.3.1

Reorder $\log (t)$ and $\frac{1}{4}$ .

$\log (r^{\frac{1}{2}}) + \log (s^{\frac{1}{3}}) - (\frac{1}{4} \log (t))$

Step 1.3.2

Simplify $\frac{1}{4} \log (t)$ by moving $\frac{1}{4}$ inside the logarithm.

$\log (r^{\frac{1}{2}}) + \log (s^{\frac{1}{3}}) - \log (t^{\frac{1}{4}})$

Step 2

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

$\log (r^{\frac{1}{2}} s^{\frac{1}{3}}) - \log (t^{\frac{1}{4}})$

Step 3

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

$\log (\frac{r^{\frac{1}{2}} s^{\frac{1}{3}}}{t^{\frac{1}{4}}})$