Trigonometry Examples

$\frac{1}{2} \cdot \log (x + 2) = 2$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot \log (x + 2)) = 2 \cdot 2$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $2 (\frac{1}{2} \cdot \log (x + 2))$ .

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Step 2.1.1.1

Combine $\frac{1}{2}$ and $\log (x + 2)$ .

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

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Cancel the common factor.

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

Step 2.1.1.2.2

Rewrite the expression.

$\log (x + 2) = 2 \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $2$ .

$\log (x + 2) = 4$

Step 3

Rewrite $\log (x + 2) = 4$ 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 $b^{y} = x$ .

$10^{4} = x + 2$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite the equation as $x + 2 = 10^{4}$ .

$x + 2 = 10^{4}$

Step 4.2

Raise $10$ to the power of $4$ .

$x + 2 = 10000$

Step 4.3

Move all terms not containing $x$ to the right side of the equation.

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Step 4.3.1

Subtract $2$ from both sides of the equation.

$x = 10000 - 2$

Step 4.3.2

Subtract $2$ from $10000$ .

$x = 9998$