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Popular >

simplify ln((x^2)/(x-1))

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 2 ln (x) - ln (x - 1)

Popular Examples

simplify-0.76-0.02958*log_{10}(1/(0.3))simplify

- 0.76 - 0.02958 \cdot lo g_{10} (\frac{1}{0.3})

simplify log_{2}(1/(0.032))+1 simplify

lo g_{2} (\frac{1}{0.032}) + 1

simplify 2ln(x^4)-3ln(x^2)+4ln(x^3)simplify

2 ln (x^{4}) - 3 ln (x^{2}) + 4 ln (x^{3})

expand log_{9}((81sqrt(y))/(x^5z^9))expand

lo g_{9} (\frac{81 y}{x ^{5} z ^{9}})

expand 2-(0, 25693/6)log_{e}(10^{-4})expand

2 - (0, \frac{25693}{6}) lo g_{e} (1 0^{- 4})

Frequently Asked Questions (FAQ)

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