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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

lo g_{10} (\frac{x ^{3} y}{z}) = lo g_{10} (x^{3} y) - lo g_{10} (z)

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

Apply log rule:

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

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

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

0.0296 \cdot 46 e^{(\frac{l n ( 263 ) - l n ( 46 )}{30}) 3}

- \frac{1}{2} ln ∣ v + 2 ∣ + \frac{1}{2} ln ∣ v ∣

ln (\frac{1}{a} e^{- \frac{y}{a}})

ln (y) - ln (11 - y)

0.0296 \cdot 46 e^{(\frac{l n ( 263 ) - l n ( 46 )}{30}) 2}

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