What is ln|10-0.9x^2|-ln|10-0.9x_{0}| ?

The solution to ln|10-0.9x^2|-ln|10-0.9x_{0}| is ln((|10-0.9x^2|)/(|10-0.9x_{0)|})

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simplify ln|10-0.9x^2|-ln|10-0.9x_{0}|

simplify

ln 10 - 0.9 x^{2} - ln ∣ 10 - 0.9 x_{0} ∣

ln (\frac{10 - 0.9 x ^{2}}{∣ 10 - 0.9 x _{0} ∣})

Solution steps

ln 10 - 0.9 x^{2} - ln ∣ 10 - 0.9 x_{0} ∣

Apply log rule:

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

ln 10 - 0.9 x^{2} - ln ∣ 10 - 0.9 x_{0} ∣ = ln (\frac{- 0.9 x ^{2} + 10}{∣ - 0.9 x _{0} + 10 ∣})

= ln (\frac{10 - 0.9 x ^{2}}{∣ 10 - 0.9 x _{0} ∣})

lo g_{9} (\frac{8 ^{2}}{5 ^{4}})

4 lo g_{3} (x) + 2 lo g_{3} (y)

ln (x + x^{2} + 1) + ln (- x + - x^{2} + 1)

2.69 - \frac{0.02569}{2} ln (\frac{0. 4 ^{3}}{2 ^{2}})

\frac{1}{3} ln (5)

What is ln|10-0.9x^2|-ln|10-0.9x_{0}| ?
The solution to ln|10-0.9x^2|-ln|10-0.9x_{0}| is ln((|10-0.9x^2|)/(|10-0.9x_{0)|})