What is 3log_{2}(x)-2log_{2}(y)+log_{2}(z) ?

The solution to 3log_{2}(x)-2log_{2}(y)+log_{2}(z) is log_{2}((x^3z)/(y^2))

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simplify 3log_{2}(x)-2log_{2}(y)+log_{2}(z)

simplify

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

lo g_{2} (\frac{x ^{3} z}{y ^{2}})

Solution steps

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

Apply log rule:

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

3 lo g_{2} (x) = lo g_{2} (x^{3})

= lo g_{2} (x^{3}) - 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} (x^{3}) - 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} (x^{3}) - lo g_{2} (y^{2}) = lo g_{2} (\frac{x ^{3}}{y ^{2}})

= lo g_{2} (\frac{x ^{3}}{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{x ^{3}}{y ^{2}}) + lo g_{2} (z) = lo g_{2} (\frac{x ^{3}}{y ^{2}} z)

= lo g_{2} (\frac{x ^{3}}{y ^{2}} z)

Multiply fractions:

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

= lo g_{2} (\frac{x ^{3} z}{y ^{2}})

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ln (22.08553 - 2) + 3 ln (8.905 - 1)

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What is 3log_{2}(x)-2log_{2}(y)+log_{2}(z) ?
The solution to 3log_{2}(x)-2log_{2}(y)+log_{2}(z) is log_{2}((x^3z)/(y^2))