What is log_{2}((2x-2)^2)-4log_{2}(1-x) ?

The solution to log_{2}((2x-2)^2)-4log_{2}(1-x) is log_{2}(4/((x-1)^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{2}((2x-2)^2)-4log_{2}(1-x)

simplify

lo g_{2} ((2 x - 2)^{2}) - 4 lo g_{2} (1 - x)

lo g_{2} (\frac{4}{( x - 1 ) ^{2}})

Solution steps

lo g_{2} ((2 x - 2)^{2}) - 4 lo g_{2} (1 - x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 lo g_{2} (- x + 1) = lo g_{2} ((- x + 1)^{4})

= lo g_{2} ((2 x - 2)^{2}) - lo g_{2} ((- x + 1)^{4})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{2} ((2 x - 2)^{2}) - lo g_{2} ((1 - x)^{4}) = lo g_{2} (\frac{( 2 x - 2 ) ^{2}}{( - x + 1 ) ^{4}})

= lo g_{2} (\frac{( 2 x - 2 ) ^{2}}{( 1 - x ) ^{4}})

Simplify

\frac{( 2 x - 2 ) ^{2}}{( 1 - x ) ^{4}} : \frac{4}{( x - 1 ) ^{2}}

= lo g_{2} (\frac{4}{( x - 1 ) ^{2}})

- lo g_{10} (2.5 x \cdot 1 0^{- 7})

ln (96 x)

lo g_{5} (2 x)

ln (e x^{4})

ln (\frac{( 3.14 x ^{3.124} )}{0.32})

What is log_{2}((2x-2)^2)-4log_{2}(1-x) ?
The solution to log_{2}((2x-2)^2)-4log_{2}(1-x) is log_{2}(4/((x-1)^2))