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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- 2 (lo g_{10} (15) + \frac{1}{2} \cdot lo g_{10} (\frac{1}{9}))

lo g_{3} (x) - lo g_{3} (x^{8})

6 lo g_{8} (11) - 30 lo g_{8} (3)

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

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