What is 20log_{10}(3u)-4log_{10}(3v) ?

The solution to 20log_{10}(3u)-4log_{10}(3v) is log_{10}((43046721u^{20})/(v^4))

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simplify 20log_{10}(3u)-4log_{10}(3v)

simplify

20 lo g_{10} (3 u) - 4 lo g_{10} (3 v)

lo g_{10} (\frac{43046721 u ^{20}}{v ^{4}})

Solution steps

20 lo g_{10} (3 u) - 4 lo g_{10} (3 v)

Apply log rule:

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

20 lo g_{10} (3 u) = lo g_{10} ((3 u)^{20})

= lo g_{10} ((3 u)^{20}) - 4 lo g_{10} (3 v)

Apply log rule:

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

4 lo g_{10} (3 v) = lo g_{10} ((3 v)^{4})

= lo g_{10} ((3 u)^{20}) - lo g_{10} ((3 v)^{4})

Apply log rule:

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

lo g_{10} ((3 u)^{20}) - lo g_{10} ((3 v)^{4}) = lo g_{10} (\frac{( 3 u ) ^{20}}{( 3 v ) ^{4}})

= lo g_{10} (\frac{( 3 u ) ^{20}}{( 3 v ) ^{4}})

Simplify

\frac{( 3 u ) ^{20}}{( 3 v ) ^{4}} : \frac{43046721 u ^{20}}{v ^{4}}

= lo g_{10} (\frac{43046721 u ^{20}}{v ^{4}})

lo g_{e} (k \cdot e^{- a \cdot x})

ln (\frac{2 e ^{3 x}}{3})

64800 e^{211 l n (\frac{80}{81})}

ln (\frac{1 + e ^{- x}}{1 + e ^{x}})

lo g_{10} (x^{2} y^{5} z)

What is 20log_{10}(3u)-4log_{10}(3v) ?
The solution to 20log_{10}(3u)-4log_{10}(3v) is log_{10}((43046721u^{20})/(v^4))