Algebra Examples

$\log_{b} (4) + \log_{b} (x - 3) - 4 \log_{b} (y)$

Step 1

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

$\log_{b} (4 (x - 3)) - 4 \log_{b} (y)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\log_{b} (4 x + 4 \cdot - 3) - 4 \log_{b} (y)$

Step 2.2

Multiply $4$ by $- 3$ .

$\log_{b} (4 x - 12) - 4 \log_{b} (y)$

Step 2.3

Simplify $- 4 \log_{b} (y)$ by moving $4$ inside the logarithm.

$\log_{b} (4 x - 12) - \log_{b} (y^{4})$

Step 3

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

$\log_{b} (\frac{4 x - 12}{y^{4}})$

Step 4

Factor $4$ out of $4 x - 12$ .

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Step 4.1

Factor $4$ out of $4 x$ .

$\log_{b} (\frac{4 (x) - 12}{y^{4}})$

Step 4.2

Factor $4$ out of $- 12$ .

$\log_{b} (\frac{4 x + 4 \cdot - 3}{y^{4}})$

Step 4.3

Factor $4$ out of $4 x + 4 \cdot - 3$ .

$\log_{b} (\frac{4 (x - 3)}{y^{4}})$