Algebra Examples

$\log_{\frac{1}{2}} (n) = - 2$

Step 1

Rewrite $\log_{\frac{1}{2}} (n) = - 2$ 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 $b^{y} = x$ .

${(\frac{1}{2})}^{- 2} = n$

Step 2

Solve for $n$ .

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Step 2.1

Rewrite the equation as $n = {(\frac{1}{2})}^{- 2}$ .

$n = {(\frac{1}{2})}^{- 2}$

Step 2.2

Simplify ${(\frac{1}{2})}^{- 2}$ .

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Step 2.2.1

Change the sign of the exponent by rewriting the base as its reciprocal.

$n = 2^{2}$

Step 2.2.2

Raise $2$ to the power of $2$ .

$n = 4$