What is log_{10}(x)+log_{10}(x+3)-2log_{10}(x+1) ?

The solution to log_{10}(x)+log_{10}(x+3)-2log_{10}(x+1) is log_{10}((x(x+3))/((x+1)^2))

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simplify log_{10}(x)+log_{10}(x+3)-2log_{10}(x+1)

simplify

lo g_{10} (x) + lo g_{10} (x + 3) - 2 lo g_{10} (x + 1)

lo g_{10} (\frac{x ( x + 3 )}{( x + 1 ) ^{2}})

Solution steps

lo g_{10} (x) + lo g_{10} (x + 3) - 2 lo g_{10} (x + 1)

Apply log rule:

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

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

= lo g_{10} (x (x + 3)) - 2 lo g_{10} (x + 1)

Apply log rule:

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

2 lo g_{10} (x + 1) = lo g_{10} ((x + 1)^{2})

= lo g_{10} (x (x + 3)) - lo g_{10} ((x + 1)^{2})

Apply log rule:

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

lo g_{10} (x (x + 3)) - lo g_{10} ((x + 1)^{2}) = lo g_{10} (\frac{x ( x + 3 )}{( x + 1 ) ^{2}})

= lo g_{10} (\frac{x ( x + 3 )}{( x + 1 ) ^{2}})

- \frac{1}{3} + \frac{1}{3} ln (\frac{3 + 5}{2})

3 ln (2) - 2 ln (3)

\frac{6 ln ( 3 ) - 10 ln ( 2 )}{2}

\frac{1}{2} ln (\frac{2}{2})

ln (\frac{7 x ^{5}}{y ^{3}})

What is log_{10}(x)+log_{10}(x+3)-2log_{10}(x+1) ?
The solution to log_{10}(x)+log_{10}(x+3)-2log_{10}(x+1) is log_{10}((x(x+3))/((x+1)^2))