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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{b} (2 x)

lo g_{2} (A) + lo g_{2} (B) - 2 lo g_{2} (C)

ln (\frac{3}{5})

lo g_{10} (x) + lo g_{10} (y)

ln (10) - ln (2)

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