What is expand log_{10}(x^3y^4z) ?

The solution to expand log_{10}(x^3y^4z) is 3log_{10}(x)+4log_{10}(y)+log_{10}(z)

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expand log_{10}(x^3y^4z)

expand

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

3 lo g_{10} (x) + 4 lo g_{10} (y) + lo g_{10} (z)

Solution steps

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (x^{3} y^{4} z) = lo g_{10} (x^{3}) + lo g_{10} (y^{4}) + lo g_{10} (z)

= lo g_{10} (x^{3}) + lo g_{10} (y^{4}) + lo g_{10} (z)

Apply log rule:

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

lo g_{10} (x^{3}) = 3 lo g_{10} (x)

= 3 lo g_{10} (x) + lo g_{10} (y^{4}) + lo g_{10} (z)

Apply log rule:

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

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

= 3 lo g_{10} (x) + 4 lo g_{10} (y) + lo g_{10} (z)

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

ln (\frac{1.5}{1.2})

- lo g_{10} (6.5 \cdot 1 0^{- 10})

ln (2 e^{y})

ln (\frac{x}{y ^{3}})

What is expand log_{10}(x^3y^4z) ?
The solution to expand log_{10}(x^3y^4z) is 3log_{10}(x)+4log_{10}(y)+log_{10}(z)