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

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

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

simplify

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

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

Solution steps

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

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

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

ln (5) - ln (7)

3 ln (x) + 5 ln (z)

ln (\frac{x}{x ^{2} + 6})

lo g_{5} (\frac{x}{x + 1})

lo g_{10} (\frac{10 z}{4})

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