What is ln(x-3)+ln(x+5)-2ln(x) ?

The solution to ln(x-3)+ln(x+5)-2ln(x) is ln(((x-3)(x+5))/(x^2))

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simplify ln(x-3)+ln(x+5)-2ln(x)

simplify

ln (x - 3) + ln (x + 5) - 2 ln (x)

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

Solution steps

ln (x - 3) + ln (x + 5) - 2 ln (x)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (x - 3) + ln (x + 5) = ln ((x - 3) (x + 5))

= ln ((x - 3) (x + 5)) - 2 ln (x)

Apply log rule:

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

2 ln (x) = ln (x^{2})

= ln ((x - 3) (x + 5)) - ln (x^{2})

Apply log rule:

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

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

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

ln (e^{5 x + 9}) - 4 ln^{3 x + 6} (x)

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

25 lo g_{2} (1 + 1010)

lo g_{x} ((4 x + 1)^{3})

ln (\frac{573.15}{293.15})

What is ln(x-3)+ln(x+5)-2ln(x) ?
The solution to ln(x-3)+ln(x+5)-2ln(x) is ln(((x-3)(x+5))/(x^2))