What is 8log_{5}(u)+2log_{5}(v) ?

The solution to 8log_{5}(u)+2log_{5}(v) is log_{5}(u^8v^2)

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simplify 8log_{5}(u)+2log_{5}(v)

simplify

8 lo g_{5} (u) + 2 lo g_{5} (v)

lo g_{5} (u^{8} v^{2})

Solution steps

8 lo g_{5} (u) + 2 lo g_{5} (v)

Apply log rule:

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

8 lo g_{5} (u) = lo g_{5} (u^{8})

= lo g_{5} (u^{8}) + 2 lo g_{5} (v)

Apply log rule:

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

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

= lo g_{5} (u^{8}) + lo g_{5} (v^{2})

Apply log rule:

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

lo g_{5} (u^{8}) + lo g_{5} (v^{2}) = lo g_{5} (u^{8} v^{2})

= lo g_{5} (u^{8} v^{2})

ln (\frac{6 x - 1}{2 x ^{3} + 4 x})

6 ln (\frac{6}{5})

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

0.5 ln (400 + x) + 0.5 ln (- 400 + x)

lo g_{e} (362)

What is 8log_{5}(u)+2log_{5}(v) ?
The solution to 8log_{5}(u)+2log_{5}(v) is log_{5}(u^8v^2)