What is log_{2}(2x)-2log_{2}(y)+log_{2}(z) ?

The solution to log_{2}(2x)-2log_{2}(y)+log_{2}(z) is log_{2}((2xz)/(y^2))

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simplify log_{2}(2x)-2log_{2}(y)+log_{2}(z)

simplify

lo g_{2} (2 x) - 2 lo g_{2} (y) + lo g_{2} (z)

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

Solution steps

lo g_{2} (2 x) - 2 lo g_{2} (y) + lo g_{2} (z)

Apply log rule:

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

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

= lo g_{2} (2 x) - lo g_{2} (y^{2}) + lo g_{2} (z)

Apply log rule:

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

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

= lo g_{2} (\frac{2 x}{y ^{2}}) + lo g_{2} (z)

Apply log rule:

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

lo g_{2} (\frac{2 x}{y ^{2}}) + lo g_{2} (z) = lo g_{2} (\frac{2 x}{y ^{2}} z)

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

5 ln (\frac{6.5}{6})

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What is log_{2}(2x)-2log_{2}(y)+log_{2}(z) ?
The solution to log_{2}(2x)-2log_{2}(y)+log_{2}(z) is log_{2}((2xz)/(y^2))