Precalculus Examples

$\frac{1}{3} \cdot \frac{\log_{5} (p) \cdot 1}{4} \cdot \log_{5} (q) - 2 \log_{5} (t)$

Step 1

Rewrite $\frac{\log_{5} (p) \cdot 1}{4}$ as $\frac{1}{4} \log_{5} (p)$ .

$\frac{1}{3} \cdot (\frac{1}{4} \log_{5} (p)) \cdot \log_{5} (q) - 2 \log_{5} (t)$

Step 2

Simplify $\frac{1}{4} \log_{5} (p)$ by moving $\frac{1}{4}$ inside the logarithm.

$\frac{1}{3} \cdot \log_{5} (p^{\frac{1}{4}}) \cdot \log_{5} (q) - 2 \log_{5} (t)$

Step 3

Simplify $\frac{1}{3} \log_{5} (p^{\frac{1}{4}})$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{5} ({(p^{\frac{1}{4}})}^{\frac{1}{3}}) \cdot \log_{5} (q) - 2 \log_{5} (t)$

Step 4

Multiply the exponents in ${(p^{\frac{1}{4}})}^{\frac{1}{3}}$ .

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Step 4.1

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

$\log_{5} (p^{\frac{1}{4} \cdot \frac{1}{3}}) \cdot \log_{5} (q) - 2 \log_{5} (t)$

Step 4.2

Multiply $\frac{1}{4} \cdot \frac{1}{3}$ .

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Step 4.2.1

Multiply $\frac{1}{4}$ by $\frac{1}{3}$ .

$\log_{5} (p^{\frac{1}{4 \cdot 3}}) \cdot \log_{5} (q) - 2 \log_{5} (t)$

Step 4.2.2

Multiply $4$ by $3$ .

$\log_{5} (p^{\frac{1}{12}}) \cdot \log_{5} (q) - 2 \log_{5} (t)$

Step 5

Simplify $- 2 \log_{5} (t)$ by moving $2$ inside the logarithm.

$\log_{5} (p^{\frac{1}{12}}) \log_{5} (q) - \log_{5} (t^{2})$