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

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

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simplify log_{10}((x(x+6))/((x+5)^6))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

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

lo g_{5} (\frac{x}{x + 2})

2 lo g_{10} (x y)

ln (7 x^{5})

ln (x + 3) + ln (x - 2)

ln (y) - ln (x) - ln (e)

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