What is 5log_{7}(u)+2log_{7}(v) ?

The solution to 5log_{7}(u)+2log_{7}(v) is log_{7}(u^5v^2)

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simplify 5log_{7}(u)+2log_{7}(v)

simplify

5 lo g_{7} (u) + 2 lo g_{7} (v)

lo g_{7} (u^{5} v^{2})

Solution steps

5 lo g_{7} (u) + 2 lo g_{7} (v)

Apply log rule:

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

5 lo g_{7} (u) = lo g_{7} (u^{5})

= lo g_{7} (u^{5}) + 2 lo g_{7} (v)

Apply log rule:

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

2 lo g_{7} (v) = lo g_{7} (v^{2})

= lo g_{7} (u^{5}) + lo g_{7} (v^{2})

Apply log rule:

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

lo g_{7} (u^{5}) + lo g_{7} (v^{2}) = lo g_{7} (u^{5} v^{2})

= lo g_{7} (u^{5} v^{2})

3 lo g_{10} (x) + lo g_{10} (z) - 2 lo g_{10} (y)

lo g_{2} (\frac{x}{1 - x})

ln (2 x) + 2 x ln (2 x)

lo g_{10} (10 x x - 3)

lo g_{6} (216 x)

What is 5log_{7}(u)+2log_{7}(v) ?
The solution to 5log_{7}(u)+2log_{7}(v) is log_{7}(u^5v^2)