What is 3log_{2}(x)-4log_{2}(y)+2log_{2}(z) ?

The solution to 3log_{2}(x)-4log_{2}(y)+2log_{2}(z) is log_{2}((x^3z^2)/(y^4))

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simplify 3log_{2}(x)-4log_{2}(y)+2log_{2}(z)

simplify

3 lo g_{2} (x) - 4 lo g_{2} (y) + 2 lo g_{2} (z)

lo g_{2} (\frac{x ^{3} z ^{2}}{y ^{4}})

Solution steps

3 lo g_{2} (x) - 4 lo g_{2} (y) + 2 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}) - 4 lo g_{2} (y) + 2 lo g_{2} (z)

Apply log rule:

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

4 lo g_{2} (y) = lo g_{2} (y^{4})

= lo g_{2} (x^{3}) - lo g_{2} (y^{4}) + 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^{4}) = lo g_{2} (\frac{x ^{3}}{y ^{4}})

= lo g_{2} (\frac{x ^{3}}{y ^{4}}) + 2 lo g_{2} (z)

Apply log rule:

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

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

= lo g_{2} (\frac{x ^{3}}{y ^{4}}) + lo g_{2} (z^{2})

Apply log rule:

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

lo g_{2} (\frac{x ^{3}}{y ^{4}}) + lo g_{2} (z^{2}) = lo g_{2} (\frac{x ^{3}}{y ^{4}} z^{2})

= lo g_{2} (\frac{x ^{3}}{y ^{4}} z^{2})

Multiply fractions:

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

= lo g_{2} (\frac{x ^{3} z ^{2}}{y ^{4}})

ln (\frac{\frac{x}{2}}{x})

ln (\frac{( 1 ) ( 1 ) + 1}{( 1 )})

ln (\frac{150}{100})

lo g_{e} (x^{10} 7 - x)

ln (x + 3) + ln (1) - ln (2)

What is 3log_{2}(x)-4log_{2}(y)+2log_{2}(z) ?
The solution to 3log_{2}(x)-4log_{2}(y)+2log_{2}(z) is log_{2}((x^3z^2)/(y^4))