What is 8log_{6}(u)+7log_{6}(v) ?

The solution to 8log_{6}(u)+7log_{6}(v) is log_{6}(u^8v^7)

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simplify 8log_{6}(u)+7log_{6}(v)

simplify

8 lo g_{6} (u) + 7 lo g_{6} (v)

lo g_{6} (u^{8} v^{7})

Solution steps

8 lo g_{6} (u) + 7 lo g_{6} (v)

Apply log rule:

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

8 lo g_{6} (u) = lo g_{6} (u^{8})

= lo g_{6} (u^{8}) + 7 lo g_{6} (v)

Apply log rule:

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

7 lo g_{6} (v) = lo g_{6} (v^{7})

= lo g_{6} (u^{8}) + lo g_{6} (v^{7})

Apply log rule:

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

lo g_{6} (u^{8}) + lo g_{6} (v^{7}) = lo g_{6} (u^{8} v^{7})

= lo g_{6} (u^{8} v^{7})

10 \cdot lo g_{10} (0.64 \cdot (π \cdot \frac{6.5}{0.0103})^{2})

- ln (3) - ln (2)

- ln (\frac{2}{5730})

ln (\frac{( x - 2 ) ^{3}}{5 x ^{2} + 1 ( x + 3 ) ^{2}})

lo g_{10} (a) - 2 lo g_{10} (c)

What is 8log_{6}(u)+7log_{6}(v) ?
The solution to 8log_{6}(u)+7log_{6}(v) is log_{6}(u^8v^7)