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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{y ^{4}}{x ^{\frac{1}{2}}} : \frac{y ^{4} x}{x}

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

Apply log rule:

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

3 lo g_{a} (w) = lo g_{a} (w^{3})

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

Apply log rule:

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

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

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

Simplify

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

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

f (x) = \frac{1}{3} ln (x + 8) + \frac{1}{2} ln (x - 1)

lo g_{b} (z^{2} x)

ln (\frac{2 ( 1 ) - 3}{3 ( 1 ) - 1})

- 16 ln (2) - e^{2} + 16 ln (- 2) + \frac{160}{3} + \frac{1}{e ^{2}}

ln (\frac{- 1}{5})

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