Precalculus Examples

$6 \log_{m} (w) - \frac{1}{2} \cdot \log_{m} (x) + 2 \log_{m} (y)$

Step 1

Simplify each term.

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Step 1.1

Simplify $6 \log_{m} (w)$ by moving $6$ inside the logarithm.

$\log_{m} (w^{6}) - \frac{1}{2} \cdot \log_{m} (x) + 2 \log_{m} (y)$

Step 1.2

Multiply $- \frac{1}{2} \log_{m} (x)$ .

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Step 1.2.1

Reorder $\log_{m} (x)$ and $\frac{1}{2}$ .

$\log_{m} (w^{6}) - (\frac{1}{2} \log_{m} (x)) + 2 \log_{m} (y)$

Step 1.2.2

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

$\log_{m} (w^{6}) - \log_{m} (x^{\frac{1}{2}}) + 2 \log_{m} (y)$

Step 1.3

Simplify $2 \log_{m} (y)$ by moving $2$ inside the logarithm.

$\log_{m} (w^{6}) - \log_{m} (x^{\frac{1}{2}}) + \log_{m} (y^{2})$

Step 2

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

$\log_{m} (\frac{w^{6}}{x^{\frac{1}{2}}}) + \log_{m} (y^{2})$

Step 3

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

$\log_{m} (\frac{w^{6}}{x^{\frac{1}{2}}} y^{2})$

Step 4

Combine $\frac{w^{6}}{x^{\frac{1}{2}}}$ and $y^{2}$ .

$\log_{m} (\frac{w^{6} y^{2}}{x^{\frac{1}{2}}})$