Precalculus Examples

$3 (\log_{7} (x) + 3 \log_{7} (y) - f \log_{7} (z))$

Step 1

Simplify $3 \log_{7} (y)$ by moving $3$ inside the logarithm.

$3 (\log_{7} (x) + \log_{7} (y^{3}) - f \log_{7} (z))$

Step 2

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

$3 (\log_{7} (x y^{3}) - f \log_{7} (z))$

Step 3

Apply the distributive property.

$3 \log_{7} (x y^{3}) + 3 (- f \log_{7} (z))$

Step 4

Simplify $3 \log_{7} (x y^{3})$ by moving $3$ inside the logarithm.

$\log_{7} ({(x y^{3})}^{3}) + 3 (- f \log_{7} (z))$

Step 5

Multiply $3 (- f \log_{7} (z))$ .

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Step 5.1

Multiply $- 1$ by $3$ .

$\log_{7} ({(x y^{3})}^{3}) - 3 (f \log_{7} (z))$

Step 5.2

Simplify $- 3 \log_{7} (z)$ by moving $3$ inside the logarithm.

$\log_{7} ({(x y^{3})}^{3}) + f (- \log_{7} (z^{3}))$

Step 6

Simplify each term.

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Step 6.1

Apply the product rule to $x y^{3}$ .

$\log_{7} (x^{3} {(y^{3})}^{3}) + f (- \log_{7} (z^{3}))$

Step 6.2

Multiply the exponents in ${(y^{3})}^{3}$ .

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Step 6.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log_{7} (x^{3} y^{3 \cdot 3}) + f (- \log_{7} (z^{3}))$

Step 6.2.2

Multiply $3$ by $3$ .

$\log_{7} (x^{3} y^{9}) + f (- \log_{7} (z^{3}))$

Step 6.3

Rewrite using the commutative property of multiplication.

$\log_{7} (x^{3} y^{9}) - f \log_{7} (z^{3})$