Trigonometry Examples

$\log (P) + n \log (V) = \log (c)$

Step 1

Reorder $\log (P)$ and $n \log (V)$ .

$n \log (V) + \log (P) = \log (c)$

Step 2

Move all the terms containing a logarithm to the left side of the equation.

$n \log (V) + \log (P) - \log (c) = 0$

Step 3

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

$n \log (V) + \log (\frac{P}{c}) = 0$

Step 4

Subtract $\log (\frac{P}{c})$ from both sides of the equation.

$n \log (V) = - \log (\frac{P}{c})$

Step 5

Divide each term in $n \log (V) = - \log (\frac{P}{c})$ by $n$ and simplify.

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Step 5.1

Divide each term in $n \log (V) = - \log (\frac{P}{c})$ by $n$ .

$\frac{n \log (V)}{n} = \frac{- \log (\frac{P}{c})}{n}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $n$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{n \log (V)}{n} = \frac{- \log (\frac{P}{c})}{n}$

Step 5.2.1.2

Divide $\log (V)$ by $1$ .

$\log (V) = \frac{- \log (\frac{P}{c})}{n}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$\log (V) = - \frac{\log (\frac{P}{c})}{n}$

Step 6

Rewrite $\log (V) = - \frac{\log (\frac{P}{c})}{n}$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$10^{- \frac{\log (\frac{P}{c})}{n}} = V$

Step 7

Rewrite the equation as $V = 10^{- \frac{\log (\frac{P}{c})}{n}}$ .

$V = 10^{- \frac{\log (\frac{P}{c})}{n}}$