Trigonometry Examples

$\log (k) = c \log (v) + \log (p)$

Step 1

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

$\log (k) - c \log (v) - \log (p) = 0$

Step 2

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

$- c \log (v) + \log (\frac{k}{p}) = 0$

Step 3

Add $c \log (v)$ to both sides of the equation.

$\log (\frac{k}{p}) = c \log (v)$

Step 4

Rewrite $\log (\frac{k}{p}) = c \log (v)$ 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 $b^{y} = x$ .

$10^{c \log (v)} = \frac{k}{p}$

Step 5

Solve for $k$ .

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Step 5.1

Rewrite the equation as $\frac{k}{p} = 10^{c \log (v)}$ .

$\frac{k}{p} = 10^{c \log (v)}$

Step 5.2

Multiply both sides by $p$ .

$\frac{k}{p} p = 10^{c \log (v)} p$

Step 5.3

Simplify.

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Step 5.3.1

Simplify the left side.

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Step 5.3.1.1

Cancel the common factor of $p$ .

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Step 5.3.1.1.1

Cancel the common factor.

$\frac{k}{p} p = 10^{c \log (v)} p$

Step 5.3.1.1.2

Rewrite the expression.

$k = 10^{c \log (v)} p$

Step 5.3.2

Simplify the right side.

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Step 5.3.2.1

Reorder factors in $10^{c \log (v)} p$ .

$k = p \cdot 10^{c \log (v)}$