What is log_{10}((x(x+2))/((x+3)^2)) ?

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

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simplify log_{10}((x(x+2))/((x+3)^2))

simplify

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

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

Solution steps

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

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

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

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

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

3 ln (x + 8) - 6 ln (x^{2} + 7)

lo g_{10} ((\frac{x ^{4}}{y})^{6})

4 \cdot lo g_{10} (x) - (2 \cdot lo g_{10} (v) + 3 \cdot lo g_{10} (y))

lo g_{10} (\frac{y z ^{4}}{x})

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

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