Precalculus Examples

$(2 x \log (8)) ((x - 2) \log (\frac{1}{4})) = (- x \log (4)) ((2 - x) \log (\frac{1}{2}))$

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, $b = 10$ , $x =$ , and $y = (- x \log (4)) ((2 - x) \log (\frac{1}{2}))$ .

$b = 10$

$x =$

$y = (- x \log (4)) ((2 - x) \log (\frac{1}{2}))$

Step 2

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

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