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

The solution to 3(log_{2}(x)-4log_{2}(y))+2log_{2}(w) is log_{2}((x^3w^2)/(y^{12)})

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

simplify

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

lo g_{2} (\frac{x ^{3} w ^{2}}{y ^{12}})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

(\frac{x}{y ^{4}})^{3} w^{2} : \frac{x ^{3} w ^{2}}{y ^{12}}

= lo g_{2} (\frac{x ^{3} w ^{2}}{y ^{12}})

ln ∣ x + 1 ∣ - ln ∣ x + 2 ∣

ln (\frac{81 + 273}{22 + 273})

- lo g_{10} (2.85 \cdot 1 0^{12})

ln (\frac{215}{2})

2 lo g_{a} (t - lo g_{a} (s) + 4 lo g_{a} (u))

What is 3(log_{2}(x)-4log_{2}(y))+2log_{2}(w) ?
The solution to 3(log_{2}(x)-4log_{2}(y))+2log_{2}(w) is log_{2}((x^3w^2)/(y^{12)})