Algebra Examples

$\log_{- \frac{1}{2}} (x) = - 7$

Step 1

For logarithmic equations, $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ such that $x > 0$ , $b > 0$ , and $b \neq 1$ . In this case, $b = - \frac{1}{2}$ , $x = x$ , and $y = - 7$ .

$b = - \frac{1}{2}$

$x = x$

$y = - 7$

Step 2

Substitute the values of $b$ , $x$ , and $y$ into the equation $b^{y} = x$ .

${(- \frac{1}{2})}^{- 7} = x$