What is simplify-ln(x-3)+2ln(x-2)+C ?

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (2 x^{7})

2 lo g_{a} (3 x^{4}) - \frac{1}{2} lo g_{a} (3 x + 7)

2^{\frac{l n ( \frac{7}{4} )}{2 l n ( 2 )}}

lo g_{10} (K) + 3 lo g_{10} (L) - 5 lo g_{10} (T)

10 \cdot lo g_{10} (\frac{5 \cdot 1 0 ^{- 3}}{1})

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