Algebra Examples

$2 \log_{b} (u) + 3 \log_{b} (v) - \frac{1}{2} \log_{b} (w)$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log_{b} (u)$ by moving $2$ inside the logarithm.

$\log_{b} (u^{2}) + 3 \log_{b} (v) - \frac{1}{2} \cdot \log_{b} (w)$

Step 1.2

Simplify $3 \log_{b} (v)$ by moving $3$ inside the logarithm.

$\log_{b} (u^{2}) + \log_{b} (v^{3}) - \frac{1}{2} \cdot \log_{b} (w)$

Step 1.3

Multiply $- \frac{1}{2} \log_{b} (w)$ .

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Step 1.3.1

Reorder $\log_{b} (w)$ and $\frac{1}{2}$ .

$\log_{b} (u^{2}) + \log_{b} (v^{3}) - (\frac{1}{2} \log_{b} (w))$

Step 1.3.2

Simplify $\frac{1}{2} \log_{b} (w)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{b} (u^{2}) + \log_{b} (v^{3}) - \log_{b} (w^{\frac{1}{2}})$

Step 2

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

$\log_{b} (u^{2} v^{3}) - \log_{b} (w^{\frac{1}{2}})$

Step 3

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

$\log_{b} (\frac{u^{2} v^{3}}{w^{\frac{1}{2}}})$