Solve for n log base 1/2 of n=-2

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

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 $n$ .

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

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

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

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

$n = 2^{2}$

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

$n = 4$

Solve for n log base 1/2 of n=-2

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