What is log_{10}(x)+2log_{10}(y-3) ?

The solution to log_{10}(x)+2log_{10}(y-3) is log_{10}(x(y-3)^2)

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simplify log_{10}(x)+2log_{10}(y-3)

simplify

lo g_{10} (x) + 2 lo g_{10} (y - 3)

lo g_{10} (x (y - 3)^{2})

Solution steps

lo g_{10} (x) + 2 lo g_{10} (y - 3)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{10} (x) + lo g_{10} ((y - 3)^{2})

Apply log rule:

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

lo g_{10} (x) + lo g_{10} ((y - 3)^{2}) = lo g_{10} (x (y - 3)^{2})

= lo g_{10} (x (y - 3)^{2})

lo g_{3} (\frac{x ^{3}}{y ^{5} 81})

ln (\frac{1}{25 k})

ln (\frac{x}{2 + 2})

ln (\frac{50}{5})

What is log_{10}(x)+2log_{10}(y-3) ?
The solution to log_{10}(x)+2log_{10}(y-3) is log_{10}(x(y-3)^2)