What is expand log_{10}((sqrt(x^2-4))/((x+3)^2)) ?

The solution to expand log_{10}((sqrt(x^2-4))/((x+3)^2)) is log_{10}(sqrt(x^2-4))-2log_{10}(x+3)

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expand log_{10}((sqrt(x^2-4))/((x+3)^2))

expand

lo g_{10} (\frac{x ^{2} - 4}{( x + 3 ) ^{2}})

lo g_{10} (x^{2} - 4) - 2 lo g_{10} (x + 3)

Solution steps

lo g_{10} (\frac{x ^{2} - 4}{( x + 3 ) ^{2}})

Apply log rule:

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

lo g_{10} (\frac{x ^{2} - 4}{( x + 3 ) ^{2}}) = lo g_{10} (x^{2} - 4) - lo g_{10} ((x + 3)^{2})

= lo g_{10} (x^{2} - 4) - lo g_{10} ((x + 3)^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= lo g_{10} (x^{2} - 4) - 2 lo g_{10} (x + 3)

- lo g_{10} (3.46 \cdot 1 0^{- 7})

ln (θ e^{(θ - 1) l n (x)})

ln (\frac{2 x - 3}{x ^{2} - 5 x})

(- \frac{1}{3}) ln (\frac{1}{3})

2 ln ∣ 4 ∣ + \frac{3}{4} + 3 ln ∣ 5 ∣

What is expand log_{10}((sqrt(x^2-4))/((x+3)^2)) ?
The solution to expand log_{10}((sqrt(x^2-4))/((x+3)^2)) is log_{10}(sqrt(x^2-4))-2log_{10}(x+3)