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

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

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

simplify

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

ln (\frac{u ^{10}}{v ^{2}})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

2 lo g_{e} (v) = lo g_{e} (v^{2})

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (\frac{u ^{10}}{v ^{2}})

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