What is 3log_{2}(z)-1/2 log_{2}(x)+4log_{2}(w) ?

The solution to 3log_{2}(z)-1/2 log_{2}(x)+4log_{2}(w) is log_{2}((z^3w^4sqrt(x))/x)

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simplify 3log_{2}(z)-1/2 log_{2}(x)+4log_{2}(w)

simplify

3 lo g_{2} (z) - \frac{1}{2} lo g_{2} (x) + 4 lo g_{2} (w)

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

Solution steps

3 lo g_{2} (z) - \frac{1}{2} lo g_{2} (x) + 4 lo g_{2} (w)

Apply log rule:

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

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

= lo g_{2} (z^{3}) - \frac{1}{2} lo g_{2} (x) + 4 lo g_{2} (w)

Apply log rule:

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

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

= lo g_{2} (z^{3}) - lo g_{2} (x^{\frac{1}{2}}) + 4 lo g_{2} (w)

Apply log rule:

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

lo g_{2} (z^{3}) - lo g_{2} (x^{\frac{1}{2}}) = lo g_{2} (\frac{z ^{3}}{x ^{\frac{1}{2}}})

= lo g_{2} (\frac{z ^{3}}{x ^{\frac{1}{2}}}) + 4 lo g_{2} (w)

Simplify

\frac{z ^{3}}{x ^{\frac{1}{2}}} : \frac{z ^{3} x}{x}

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{z ^{3} x}{x} w^{4} : \frac{z ^{3} w ^{4} x}{x}

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

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

ln (31 x^{5} y)

lo g_{2} (6) + lo g_{2} (12)

lo g_{10} (\frac{x}{y ^{9} z ^{5}})

lo g_{4} (11) - lo g_{4} (9)

What is 3log_{2}(z)-1/2 log_{2}(x)+4log_{2}(w) ?
The solution to 3log_{2}(z)-1/2 log_{2}(x)+4log_{2}(w) is log_{2}((z^3w^4sqrt(x))/x)