What is 3log_{5}(u)-3log_{5}(v) ?

The solution to 3log_{5}(u)-3log_{5}(v) is log_{5}((u^3)/(v^3))

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simplify 3log_{5}(u)-3log_{5}(v)

simplify

3 lo g_{5} (u) - 3 lo g_{5} (v)

lo g_{5} (\frac{u ^{3}}{v ^{3}})

Solution steps

3 lo g_{5} (u) - 3 lo g_{5} (v)

Apply log rule:

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

3 lo g_{5} (u) = lo g_{5} (u^{3})

= lo g_{5} (u^{3}) - 3 lo g_{5} (v)

Apply log rule:

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

3 lo g_{5} (v) = lo g_{5} (v^{3})

= lo g_{5} (u^{3}) - lo g_{5} (v^{3})

Apply log rule:

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

lo g_{5} (u^{3}) - lo g_{5} (v^{3}) = lo g_{5} (\frac{u ^{3}}{v ^{3}})

= lo g_{5} (\frac{u ^{3}}{v ^{3}})

lo g_{10} (\frac{\frac{1}{( 1 + c o t ^{2} ( x ) ) ^{1}}}{2})

ln (\frac{1}{40})

ln (\frac{23138}{1500})

2 (ln (\frac{x - 25}{25} + 1) - ln (\frac{x - 25}{25} - 1))

ln (40) - ln (400)

What is 3log_{5}(u)-3log_{5}(v) ?
The solution to 3log_{5}(u)-3log_{5}(v) is log_{5}((u^3)/(v^3))