Trigonometry Examples

$3 \log (p) - (2 \log (t + \frac{1}{2} \cdot \log (r)))$

Step 1

Simplify each term.

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Step 1.1

Simplify $3 \log (p)$ by moving $3$ inside the logarithm.

$\log (p^{3}) - (2 \log (t + \frac{1}{2} \cdot \log (r)))$

Step 1.2

Simplify $\frac{1}{2} \log (r)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log (p^{3}) - (2 \log (t + \log (r^{\frac{1}{2}})))$

Step 1.3

Simplify $2 \log (t + \log (r^{\frac{1}{2}}))$ by moving $2$ inside the logarithm.

$\log (p^{3}) - \log ({(t + \log (r^{\frac{1}{2}}))}^{2})$

Step 2

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

$\log (\frac{p^{3}}{{(t + \log (r^{\frac{1}{2}}))}^{2}})$