What is 2log_{10}(u)-4log_{10}(v) ?

The solution to 2log_{10}(u)-4log_{10}(v) is log_{10}((u^2)/(v^4))

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simplify 2log_{10}(u)-4log_{10}(v)

simplify

2 lo g_{10} (u) - 4 lo g_{10} (v)

lo g_{10} (\frac{u ^{2}}{v ^{4}})

Solution steps

2 lo g_{10} (u) - 4 lo g_{10} (v)

Apply log rule:

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

2 lo g_{10} (u) = lo g_{10} (u^{2})

= lo g_{10} (u^{2}) - 4 lo g_{10} (v)

Apply log rule:

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

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

= lo g_{10} (u^{2}) - lo g_{10} (v^{4})

Apply log rule:

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

lo g_{10} (u^{2}) - lo g_{10} (v^{4}) = lo g_{10} (\frac{u ^{2}}{v ^{4}})

= lo g_{10} (\frac{u ^{2}}{v ^{4}})

- lo g_{10} (7.5 \times 1 0^{- 3})

ln (\frac{x ^{2}}{x ( 1 + x ) ^{4}})

- lo g_{10} (3 \times 1 0^{- 4})

- lo g_{10} (6.2 \times 1 0^{- 8})

lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{2}})

What is 2log_{10}(u)-4log_{10}(v) ?
The solution to 2log_{10}(u)-4log_{10}(v) is log_{10}((u^2)/(v^4))