What is log_{a}(3xy)-5log_{10}(a)(y+2) ?

The solution to log_{a}(3xy)-5log_{10}(a)(y+2) is log_{a}(3)+log_{a}(x)+log_{a}(y)-5log_{10}(a)(y+2)

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simplify log_{a}(3xy)-5log_{10}(a)(y+2)

simplify

lo g_{a} (3 x y) - 5 lo g_{10} (a) (y + 2)

lo g_{a} (3) + lo g_{a} (x) + lo g_{a} (y) - 5 lo g_{10} (a) (y + 2)

Solution steps

lo g_{a} (3 x y) - 5 lo g_{10} (a) (y + 2)

Apply log rule:

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

lo g_{a} (3 x y) = lo g_{a} (3) + lo g_{a} (x) + lo g_{a} (y)

= lo g_{a} (3) + lo g_{a} (x) + lo g_{a} (y) - 5 lo g_{10} (a) (y + 2)

lo g_{3} (4 x y)

lo g_{10} (\frac{9 x ^{4} y}{5 y})

lo g_{2} (x x^{2} + 1)

\frac{2}{3} ln (4) - \frac{1}{3} ln (7)

3 lo g_{10} (x^{3}) + lo g_{10} (x) - lo g_{10} (x^{4})

What is log_{a}(3xy)-5log_{10}(a)(y+2) ?
The solution to log_{a}(3xy)-5log_{10}(a)(y+2) is log_{a}(3)+log_{a}(x)+log_{a}(y)-5log_{10}(a)(y+2)