What is expand log_{10}((6w^5)/x) ?

The solution to expand log_{10}((6w^5)/x) is log_{10}(6)+5log_{10}(w)-log_{10}(x)

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expand log_{10}((6w^5)/x)

expand

lo g_{10} (\frac{6 w ^{5}}{x})

lo g_{10} (6) + 5 lo g_{10} (w) - lo g_{10} (x)

Solution steps

lo g_{10} (\frac{6 w ^{5}}{x})

Apply log rule:

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

lo g_{10} (\frac{6 w ^{5}}{x}) = lo g_{10} (6 w^{5}) - lo g_{10} (x)

= lo g_{10} (6 w^{5}) - lo g_{10} (x)

Apply log rule:

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

lo g_{10} (6 w^{5}) = lo g_{10} (6) + lo g_{10} (w^{5})

= lo g_{10} (6) + lo g_{10} (w^{5}) - lo g_{10} (x)

Apply log rule:

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

lo g_{10} (w^{5}) = 5 lo g_{10} (w)

= lo g_{10} (6) + 5 lo g_{10} (w) - lo g_{10} (x)

ln (\frac{729}{10000})

lo g_{2} (x^{2}) - 5 \cdot lo g_{2} (x) + 4

5 ln (5 x)

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

ln (\frac{4 + 3 ( 12 )}{3}) - ln (\frac{4 + 3 ( 6 )}{3})

What is expand log_{10}((6w^5)/x) ?
The solution to expand log_{10}((6w^5)/x) is log_{10}(6)+5log_{10}(w)-log_{10}(x)