What is 4log_{2}(z)-1/2 log_{2}(w)+6log_{2}(y) ?

The solution to 4log_{2}(z)-1/2 log_{2}(w)+6log_{2}(y) is log_{2}((z^4y^6sqrt(w))/w)

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simplify 4log_{2}(z)-1/2 log_{2}(w)+6log_{2}(y)

simplify

4 lo g_{2} (z) - \frac{1}{2} lo g_{2} (w) + 6 lo g_{2} (y)

lo g_{2} (\frac{z ^{4} y ^{6} w}{w})

Solution steps

4 lo g_{2} (z) - \frac{1}{2} lo g_{2} (w) + 6 lo g_{2} (y)

Apply log rule:

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

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

= lo g_{2} (z^{4}) - \frac{1}{2} lo g_{2} (w) + 6 lo g_{2} (y)

Apply log rule:

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

\frac{1}{2} lo g_{2} (w) = lo g_{2} (w^{\frac{1}{2}})

= lo g_{2} (z^{4}) - lo g_{2} (w^{\frac{1}{2}}) + 6 lo g_{2} (y)

Apply log rule:

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

lo g_{2} (z^{4}) - lo g_{2} (w^{\frac{1}{2}}) = lo g_{2} (\frac{z ^{4}}{w ^{\frac{1}{2}}})

= lo g_{2} (\frac{z ^{4}}{w ^{\frac{1}{2}}}) + 6 lo g_{2} (y)

Simplify

\frac{z ^{4}}{w ^{\frac{1}{2}}} : \frac{z ^{4} w}{w}

= lo g_{2} (\frac{z ^{4} w}{w}) + 6 lo g_{2} (y)

Apply log rule:

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

6 lo g_{2} (y) = lo g_{2} (y^{6})

= lo g_{2} (\frac{z ^{4} w}{w}) + lo g_{2} (y^{6})

Apply log rule:

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

lo g_{2} (\frac{z ^{4} w}{w}) + lo g_{2} (y^{6}) = lo g_{2} (\frac{z ^{4} w}{w} y^{6})

= lo g_{2} (\frac{z ^{4} w}{w} y^{6})

Simplify

\frac{z ^{4} w}{w} y^{6} : \frac{z ^{4} y ^{6} w}{w}

= lo g_{2} (\frac{z ^{4} y ^{6} w}{w})

2 lo g_{10} (5.6) + 4 lo g_{10} (3.5)

\frac{1}{2} ln (2 \cdot 9.6 + 1) + 2 ln (9.6 - 1)

- lo g_{10} (6.46 \cdot 1 0^{- 5})

3 lo g_{10} (2) - lo g_{10} (4) + 2 lo g_{10} (5)

lo g_{e} (\frac{a + x}{x})

What is 4log_{2}(z)-1/2 log_{2}(w)+6log_{2}(y) ?
The solution to 4log_{2}(z)-1/2 log_{2}(w)+6log_{2}(y) is log_{2}((z^4y^6sqrt(w))/w)