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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

- ln (4) - ln (3)

ln (6) - ln (7)

ln (\frac{7.5}{15})

ln (x - 4) + ln (x + 4)

ln (\frac{78}{175}) - 6

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