Solve for x 1/2* log of x-2=-2

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Trigonometry

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

Multiply both sides of the equation by $2$ .

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

Simplify both sides of the equation.

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Cancel the common factor of $2$ .

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Cancel the common factor.

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

Rewrite the expression.

$1 \cdot \log (x - 2) = 2 \cdot - 2$

Multiply $\log (x - 2)$ by $1$ .

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

Multiply $2$ by $- 2$ .

$\log (x - 2) = - 4$

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 $b^{y} = x$ .

$10^{- 4} = x - 2$

Solve for $x$

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Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{10^{4}} = x - 2$

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

$\frac{1}{10000} = x - 2$

Rewrite the equation as $x - 2 = \frac{1}{10000}$ .

$x - 2 = \frac{1}{10000}$

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

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Add $2$ to both sides of the equation.

$x = \frac{1}{10000} + 2$

Simplify the right side of the equation.

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To write $\frac{2}{1}$ as a fraction with a common denominator, multiply by $\frac{10000}{10000}$ .

$x = \frac{1}{10000} + \frac{2}{1} \cdot \frac{10000}{10000}$

Write each expression with a common denominator of $10000$ , by multiplying each by an appropriate factor of $1$ .

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Combine.

$x = \frac{1}{10000} + \frac{2 \cdot 10000}{1 \cdot 10000}$

Multiply $10000$ by $1$ .

$x = \frac{1}{10000} + \frac{2 \cdot 10000}{10000}$

Combine the numerators over the common denominator.

$x = \frac{1 + 2 \cdot 10000}{10000}$

Simplify the numerator.

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Multiply $2$ by $10000$ .

$x = \frac{1 + 20000}{10000}$

Add $1$ and $20000$ .

$x = \frac{20001}{10000}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{20001}{10000}$

Decimal Form:

$x = 2.0001$

Mixed Number Form:

$x = 2 \frac{1}{10000}$

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