What is expand log_{10}(((u^2)/v)^3) ?

The solution to expand log_{10}(((u^2)/v)^3) is 3(2log_{10}(u)-log_{10}(v))

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expand log_{10}(((u^2)/v)^3)

expand

lo g_{10} ((\frac{u ^{2}}{v})^{3})

3 (2 lo g_{10} (u) - lo g_{10} (v))

Solution steps

lo g_{10} ((\frac{u ^{2}}{v})^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} ((\frac{u ^{2}}{v})^{3}) = 3 lo g_{10} (\frac{u ^{2}}{v})

= 3 lo g_{10} (\frac{u ^{2}}{v})

Apply log rule:

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

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

= 3 (lo g_{10} (u^{2}) - lo g_{10} (v))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 3 (2 lo g_{10} (u) - lo g_{10} (v))

2 lo g_{10} (m) - 3 lo g_{10} (n)

\frac{( - 4 ln ( 5 ) + 2 ln ( 3 ) )}{7 ln ( 5 ) - ln ( 3 )}

lo g_{10} (\frac{x ^{5}}{( x + 4 ) ^{3}})

3.79 + lo g_{10} (\frac{0.15 + 0.015}{0.2 - 0.015})

ln (x e^{- x^{2}})

What is expand log_{10}(((u^2)/v)^3) ?
The solution to expand log_{10}(((u^2)/v)^3) is 3(2log_{10}(u)-log_{10}(v))