What is log_{10}((x(x+2))/((x+4)^2)) ?

The solution to log_{10}((x(x+2))/((x+4)^2)) is log_{10}(x)+log_{10}(x+2)-2log_{10}(x+4)

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simplify log_{10}((x(x+2))/((x+4)^2))

simplify

lo g_{10} (\frac{x ( x + 2 )}{( x + 4 ) ^{2}})

lo g_{10} (x) + lo g_{10} (x + 2) - 2 lo g_{10} (x + 4)

Solution steps

lo g_{10} (\frac{x ( x + 2 )}{( x + 4 ) ^{2}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{x ( x + 2 )}{( x + 4 ) ^{2}}) = lo g_{10} (x (x + 2)) - lo g_{10} ((x + 4)^{2})

= lo g_{10} (x (x + 2)) - lo g_{10} ((x + 4)^{2})

lo g_{10} (x (x + 2)) = lo g_{10} (x) + lo g_{10} (x + 2)

lo g_{10} ((x + 4)^{2}) = 2 lo g_{10} (x + 4)

= lo g_{10} (x) + lo g_{10} (x + 2) - 2 lo g_{10} (x + 4)

3 ln (\frac{5}{3})

ln (6) + ln (x)

75 - 35 + 10 lo g_{10} (\frac{301}{67.2})

\frac{60 lo g _{3} ( 10 ) - 60 lo g _{3} ( 7 )}{1}

ln (\frac{23}{13})

What is log_{10}((x(x+2))/((x+4)^2)) ?
The solution to log_{10}((x(x+2))/((x+4)^2)) is log_{10}(x)+log_{10}(x+2)-2log_{10}(x+4)