What is log_{a}(5)+2log_{a}(x)+4log_{a}(y^3) ?

The solution to log_{a}(5)+2log_{a}(x)+4log_{a}(y^3) is log_{a}(5x^2y^{12})

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simplify log_{a}(5)+2log_{a}(x)+4log_{a}(y^3)

simplify

lo g_{a} (5) + 2 lo g_{a} (x) + 4 lo g_{a} (y^{3})

lo g_{a} (5 x^{2} y^{12})

Solution steps

lo g_{a} (5) + 2 lo g_{a} (x) + 4 lo g_{a} (y^{3})

Apply log rule:

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

2 lo g_{a} (x) = lo g_{a} (x^{2})

= lo g_{a} (5) + lo g_{a} (x^{2}) + 4 lo g_{a} (y^{3})

Apply log rule:

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

lo g_{a} (5) + lo g_{a} (x^{2}) = lo g_{a} (5 x^{2})

= lo g_{a} (5 x^{2}) + 4 lo g_{a} (y^{3})

Apply log rule:

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

4 lo g_{a} (y^{3}) = lo g_{a} ((y^{3})^{4})

= lo g_{a} (5 x^{2}) + lo g_{a} ((y^{3})^{4})

Apply log rule:

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

lo g_{a} (5 x^{2}) + lo g_{a} ((y^{3})^{4}) = lo g_{a} (5 x^{2} (y^{3})^{4})

= lo g_{a} (5 x^{2} (y^{3})^{4})

(y^{3})^{4} = y^{12}

= lo g_{a} (5 x^{2} y^{12})

2 lo g_{10} (\frac{D v}{v} f) - 0.8

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

ln (\frac{x}{( x + 1 ) ( x + 2 )})

\frac{1}{3} ln (\frac{5}{3} + 3)

ln (0.7721 \cdot π)

What is log_{a}(5)+2log_{a}(x)+4log_{a}(y^3) ?
The solution to log_{a}(5)+2log_{a}(x)+4log_{a}(y^3) is log_{a}(5x^2y^{12})