What is 3log_{4}(u)-6log_{4}(v) ?

The solution to 3log_{4}(u)-6log_{4}(v) is log_{4}((u^3)/(v^6))

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simplify 3log_{4}(u)-6log_{4}(v)

simplify

3 lo g_{4} (u) - 6 lo g_{4} (v)

lo g_{4} (\frac{u ^{3}}{v ^{6}})

Solution steps

3 lo g_{4} (u) - 6 lo g_{4} (v)

Apply log rule:

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

3 lo g_{4} (u) = lo g_{4} (u^{3})

= lo g_{4} (u^{3}) - 6 lo g_{4} (v)

Apply log rule:

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

6 lo g_{4} (v) = lo g_{4} (v^{6})

= lo g_{4} (u^{3}) - lo g_{4} (v^{6})

Apply log rule:

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

lo g_{4} (u^{3}) - lo g_{4} (v^{6}) = lo g_{4} (\frac{u ^{3}}{v ^{6}})

= lo g_{4} (\frac{u ^{3}}{v ^{6}})

(ln (2) - 2 ln (5)) - (ln (1) - 2 ln (4))

2 ln (x) + ln (v^{2} + 2)

ln (\frac{2 ^{- 3}}{3 ^{- 4} 5 ^{- 2}})

ln (\frac{30.3}{10.6})

- ln ∣ x ∣ - \frac{3}{x} + ln ∣ x - 1 ∣

What is 3log_{4}(u)-6log_{4}(v) ?
The solution to 3log_{4}(u)-6log_{4}(v) is log_{4}((u^3)/(v^6))