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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

\frac{1}{2} lo g_{6} (x) = lo g_{6} (x^{\frac{1}{2}})

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

Apply log rule:

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

lo g_{6} (y^{2}) - lo g_{6} (x^{\frac{1}{2}}) = lo g_{6} (\frac{y ^{2}}{x ^{\frac{1}{2}}})

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

Simplify

\frac{y ^{2}}{x ^{\frac{1}{2}}} : \frac{y ^{2} x}{x}

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

Apply log rule:

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

4 lo g_{6} (w) = lo g_{6} (w^{4})

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

Apply log rule:

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

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

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

Simplify

\frac{y ^{2} x}{x} w^{4} : \frac{y ^{2} w ^{4} x}{x}

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

lo g_{6} (\frac{( x + 3 ) ^{2}}{3 y ^{3}})

2000 [ln (5) - ln (4)]

\frac{1}{3} ln (x) - 7 ln (y) + \frac{ln ( z )}{2}

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

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