What is expand log_{10}((x^6y)/z) ?

The solution to expand log_{10}((x^6y)/z) is 6log_{10}(x)+log_{10}(y)-log_{10}(z)

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expand log_{10}((x^6y)/z)

expand

lo g_{10} (\frac{x ^{6} y}{z})

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

Solution steps

lo g_{10} (\frac{x ^{6} y}{z})

Apply log rule:

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

lo g_{10} (\frac{x ^{6} y}{z}) = lo g_{10} (x^{6} y) - lo g_{10} (z)

= lo g_{10} (x^{6} y) - lo g_{10} (z)

Apply log rule:

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

lo g_{10} (x^{6} y) = lo g_{10} (x^{6}) + lo g_{10} (y)

= lo g_{10} (x^{6}) + 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^{6}) = 6 lo g_{10} (x)

= 6 lo g_{10} (x) + lo g_{10} (y) - lo g_{10} (z)

lo g_{2} (3) + lo g_{2} (x)

ln (5 x) - ln (1)

ln (\frac{0.2}{0.1})

lo g_{5} (\frac{x ^{3}}{y ^{2}})

What is expand log_{10}((x^6y)/z) ?
The solution to expand log_{10}((x^6y)/z) is 6log_{10}(x)+log_{10}(y)-log_{10}(z)