What is 3log_{4}(u)-18log_{4}(v) ?

The solution to 3log_{4}(u)-18log_{4}(v) is log_{4}((u^3)/(v^{18)})

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simplify 3log_{4}(u)-18log_{4}(v)

simplify

3 lo g_{4} (u) - 18 lo g_{4} (v)

lo g_{4} (\frac{u ^{3}}{v ^{18}})

Solution steps

3 lo g_{4} (u) - 18 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}) - 18 lo g_{4} (v)

Apply log rule:

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

18 lo g_{4} (v) = lo g_{4} (v^{18})

= lo g_{4} (u^{3}) - lo g_{4} (v^{18})

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^{18}) = lo g_{4} (\frac{u ^{3}}{v ^{18}})

= lo g_{4} (\frac{u ^{3}}{v ^{18}})

\frac{lo g _{10} ( 2 )}{lo g _{10} ( 5 ) - lo g _{10} ( 2 )}

ln (\frac{8}{10})

2 (ln (u^{3}) + ln (w^{\frac{1}{3}}) - ln (v))

lo g_{9} (x - 5) + lo g_{9} (x + 5)

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

What is 3log_{4}(u)-18log_{4}(v) ?
The solution to 3log_{4}(u)-18log_{4}(v) is log_{4}((u^3)/(v^{18)})