What is log_{10}((x(x+4))/((x+3)^{14)}) ?

The solution to log_{10}((x(x+4))/((x+3)^{14)}) is log_{10}(x)+log_{10}(x+4)-14log_{10}(x+3)

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simplify log_{10}((x(x+4))/((x+3)^{14)})

simplify

lo g_{10} (\frac{x ( x + 4 )}{( x + 3 ) ^{14}})

lo g_{10} (x) + lo g_{10} (x + 4) - 14 lo g_{10} (x + 3)

Solution steps

lo g_{10} (\frac{x ( x + 4 )}{( x + 3 ) ^{14}})

Apply log rule:

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

lo g_{10} (\frac{x ( x + 4 )}{( x + 3 ) ^{14}}) = lo g_{10} (x (x + 4)) - lo g_{10} ((x + 3)^{14})

= lo g_{10} (x (x + 4)) - lo g_{10} ((x + 3)^{14})

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

lo g_{10} ((x + 3)^{14}) = 14 lo g_{10} (x + 3)

= lo g_{10} (x) + lo g_{10} (x + 4) - 14 lo g_{10} (x + 3)

\frac{21}{2} ln (2)

lo g_{11} (11 x)

lo g_{4} (\frac{a ^{9}}{b})

- lo g_{10} (8.24 \cdot 1 0^{- 3})

ln (- 2 e)

What is log_{10}((x(x+4))/((x+3)^{14)}) ?
The solution to log_{10}((x(x+4))/((x+3)^{14)}) is log_{10}(x)+log_{10}(x+4)-14log_{10}(x+3)