What is 2ln|x-2|-3ln|x-3| ?

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

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simplify 2ln|x-2|-3ln|x-3|

simplify

2 ln ∣ x - 2 ∣ - 3 ln ∣ x - 3 ∣

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

Solution steps

2 ln ∣ x - 2 ∣ - 3 ln ∣ x - 3 ∣

Apply log rule:

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

2 ln ∣ x - 2 ∣ = ln (∣ x - 2 ∣^{2})

= ln (∣ x - 2 ∣^{2}) - 3 ln ∣ x - 3 ∣

Apply log rule:

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

3 ln ∣ x - 3 ∣ = ln (∣ x - 3 ∣^{3})

= ln (∣ x - 2 ∣^{2}) - ln (∣ x - 3 ∣^{3})

Apply log rule:

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

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

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

∣ x - 2 ∣^{2} = (x - 2)^{2}

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

ln (x^{4} - 4) - ln (x^{2})

lo g_{7} (x (x - 10))

2 lo g_{x} (- 3 lo g_{10} (x + 1))

\frac{19.16}{0.0004 \cdot 0.02} ln (\frac{1}{1 - 0.9})

2 (lo g_{7} (x) + 3 lo g_{7} (y) - 5 lo g_{7} (z))

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