What is log_{10}(5+x)-2log_{10}(x+4) ?

The solution to log_{10}(5+x)-2log_{10}(x+4) is log_{10}((5+x)/((x+4)^2))

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simplify log_{10}(5+x)-2log_{10}(x+4)

simplify

lo g_{10} (5 + x) - 2 lo g_{10} (x + 4)

lo g_{10} (\frac{5 + x}{( x + 4 ) ^{2}})

Solution steps

lo g_{10} (5 + x) - 2 lo g_{10} (x + 4)

Apply log rule:

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

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

= lo g_{10} (x + 5) - lo g_{10} ((x + 4)^{2})

Apply log rule:

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

lo g_{10} (5 + x) - lo g_{10} ((x + 4)^{2}) = lo g_{10} (\frac{x + 5}{( x + 4 ) ^{2}})

= lo g_{10} (\frac{5 + x}{( x + 4 ) ^{2}})

lo g_{10} (x) - lo g_{10} (y)

lo g_{4} (x^{2} - 1) - 5 lo g_{4} (x + 1)

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

lo g_{10} (2 x y)

ln (x^{5}) - ln (x) + ln (\frac{1}{x})

What is log_{10}(5+x)-2log_{10}(x+4) ?
The solution to log_{10}(5+x)-2log_{10}(x+4) is log_{10}((5+x)/((x+4)^2))