What is log_{10}(116-x^2)-2log_{10}(x-1) ?

The solution to log_{10}(116-x^2)-2log_{10}(x-1) is log_{10}((116-x^2)/((x-1)^2))

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simplify log_{10}(116-x^2)-2log_{10}(x-1)

simplify

lo g_{10} (116 - x^{2}) - 2 lo g_{10} (x - 1)

lo g_{10} (\frac{116 - x ^{2}}{( x - 1 ) ^{2}})

Solution steps

lo g_{10} (116 - x^{2}) - 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^{2} + 116) - 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} (116 - x^{2}) - lo g_{10} ((x - 1)^{2}) = lo g_{10} (\frac{- x ^{2} + 116}{( x - 1 ) ^{2}})

= lo g_{10} (\frac{116 - x ^{2}}{( x - 1 ) ^{2}})

5 (ln ∣ 1 - 5 ∣ - ln ∣ 1 - 4 ∣) + 1

ln (a \cdot e^{x})

3 lo g_{a} (x) - \frac{1}{4} lo g_{a} (w) + 7 lo g_{a} (y)

- ln (7 e^{- x})

3 ln (pq) + 4 ln (p q^{2})

What is log_{10}(116-x^2)-2log_{10}(x-1) ?
The solution to log_{10}(116-x^2)-2log_{10}(x-1) is log_{10}((116-x^2)/((x-1)^2))