What is log_{2}(a)+log_{2}(b)-2log_{2}(c) ?

The solution to log_{2}(a)+log_{2}(b)-2log_{2}(c) is log_{2}((ab)/(c^2))

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simplify log_{2}(a)+log_{2}(b)-2log_{2}(c)

simplify

lo g_{2} (a) + lo g_{2} (b) - 2 lo g_{2} (c)

lo g_{2} (\frac{ab}{c ^{2}})

Solution steps

lo g_{2} (a) + lo g_{2} (b) - 2 lo g_{2} (c)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{2} (a) + lo g_{2} (b) = lo g_{2} (ab)

= lo g_{2} (ab) - 2 lo g_{2} (c)

Apply log rule:

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

2 lo g_{2} (c) = lo g_{2} (c^{2})

= lo g_{2} (ab) - lo g_{2} (c^{2})

Apply log rule:

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

lo g_{2} (ab) - lo g_{2} (c^{2}) = lo g_{2} (\frac{ab}{c ^{2}})

= lo g_{2} (\frac{ab}{c ^{2}})

\frac{1}{2} lo g_{c} (x) + 2 lo g_{c} (y) - 4 lo g_{c} (x)

ln (\frac{1}{u ^{2} + v ^{2}})

ln (x) + 3 ln (y)

ln (\frac{x + 3}{x y})

lo g_{2} (\frac{2 x ^{6}}{y})

What is log_{2}(a)+log_{2}(b)-2log_{2}(c) ?
The solution to log_{2}(a)+log_{2}(b)-2log_{2}(c) is log_{2}((ab)/(c^2))