What is (log_{5}(x+y)+2log_{5}(y))-3log_{5}(x) ?

The solution to (log_{5}(x+y)+2log_{5}(y))-3log_{5}(x) is log_{5}(((x+y)y^2)/(x^3))

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simplify (log_{5}(x+y)+2log_{5}(y))-3log_{5}(x)

simplify

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

lo g_{5} (\frac{( x + y ) y ^{2}}{x ^{3}})

Solution steps

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

Apply log rule:

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

2 lo g_{5} (y) = lo g_{5} (y^{2})

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

Apply log rule:

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

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

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

Apply log rule:

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

3 lo g_{5} (x) = lo g_{5} (x^{3})

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

Apply log rule:

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

lo g_{5} (y^{2} (x + y)) - lo g_{5} (x^{3}) = lo g_{5} (\frac{y ^{2} ( x + y )}{x ^{3}})

= lo g_{5} (\frac{( x + y ) y ^{2}}{x ^{3}})

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

2 lo g_{10} (8) - 4 lo g_{10} (x)

ln (\frac{1.308 x 1 0 ^{- 4}}{6.44 x 1 0 ^{- 3}})

ln (x) - ln (a)

What is (log_{5}(x+y)+2log_{5}(y))-3log_{5}(x) ?
The solution to (log_{5}(x+y)+2log_{5}(y))-3log_{5}(x) is log_{5}(((x+y)y^2)/(x^3))