What is expand log_{10}((3r^2)/(r-8)) ?

The solution to expand log_{10}((3r^2)/(r-8)) is log_{10}(3)+2log_{10}(r)-log_{10}(r-8)

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expand log_{10}((3r^2)/(r-8))

expand

lo g_{10} (\frac{3 r ^{2}}{r - 8})

lo g_{10} (3) + 2 lo g_{10} (r) - lo g_{10} (r - 8)

Solution steps

lo g_{10} (\frac{3 r ^{2}}{r - 8})

Apply log rule:

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

lo g_{10} (\frac{3 r ^{2}}{r - 8}) = lo g_{10} (3 r^{2}) - lo g_{10} (r - 8)

= lo g_{10} (3 r^{2}) - lo g_{10} (r - 8)

Apply log rule:

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

lo g_{10} (3 r^{2}) = lo g_{10} (3) + lo g_{10} (r^{2})

= lo g_{10} (3) + lo g_{10} (r^{2}) - lo g_{10} (r - 8)

Apply log rule:

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

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

= lo g_{10} (3) + 2 lo g_{10} (r) - lo g_{10} (r - 8)

lo g_{b} (\frac{p ^{3} q ^{5}}{m ^{3} b ^{7}})

ln (\frac{3}{8 x ^{8} y})

ln (\frac{3700}{3000})

ln (x^{13} 7 - x)

ln (\frac{4 x 1 + 2 x}{( x - 4 ) ^{3}})

What is expand log_{10}((3r^2)/(r-8)) ?
The solution to expand log_{10}((3r^2)/(r-8)) is log_{10}(3)+2log_{10}(r)-log_{10}(r-8)