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Popular >

simplify 2ln(x)-3ln(x-1)

Solution

simplify

2 ln (x) - 3 ln (x - 1)

Solution

ln (\frac{x ^{2}}{( x - 1 ) ^{3}})

Solution steps

2 ln (x) - 3 ln (x - 1)

Apply log rule:

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

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

= ln (x^{2}) - 3 ln (x - 1)

Apply log rule:

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

3 ln (x - 1) = ln ((x - 1)^{3})

= ln (x^{2}) - ln ((x - 1)^{3})

Apply log rule:

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

ln (x^{2}) - ln ((x - 1)^{3}) = ln (\frac{x ^{2}}{( x - 1 ) ^{3}})

= ln (\frac{x ^{2}}{( x - 1 ) ^{3}})

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Frequently Asked Questions (FAQ)

What is 2ln(x)-3ln(x-1) ?
The solution to 2ln(x)-3ln(x-1) is ln((x^2)/((x-1)^3))