Trigonometry Examples

$\log (x) - \log (2) = 2$

Step 1

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

$\log (\frac{x}{2}) = 2$

Step 2

Rewrite $\log (\frac{x}{2}) = 2$ 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 $b^{y} = x$ .

$10^{2} = \frac{x}{2}$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $\frac{x}{2} = 10^{2}$ .

$\frac{x}{2} = 10^{2}$

Step 3.2

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot 10^{2}$

Step 3.3

Simplify the left side.

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Step 3.3.1

Cancel the common factor of $2$ .

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Step 3.3.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot 10^{2}$

Step 3.3.1.2

Rewrite the expression.

$x = 2 \cdot 10^{2}$

Step 4

The result can be shown in multiple forms.

Scientific Notation:

$x = 2 \cdot 10^{2}$

Expanded Form:

$x = 200$