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

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

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simplify 2log_{10}(x)-log_{10}(x+4)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- 2000 ln (10) + 2000 ln (20)

\frac{1}{4} ln (y - 2) - \frac{1}{4} ln (y + 2)

\frac{( ln ( 96 ) - ln ( 3 ) )}{2}

5 ln (x - 8) - 4 ln (x)

lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{3}})

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