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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Popular Examples

simplify ln((1.2)/(1.06))simplify

ln (\frac{1.2}{1.06})

simplify-log_{10}(1.73(10^{-5}))simplify

- lo g_{10} (1.73 (1 0^{- 5}))

expand ln(10x)expand

ln (10 x)

simplify 1/6 (ln(3)-ln(5))simplify

\frac{1}{6} (ln (3) - ln (5))

simplify 2(ln(5)+ln(7))simplify

2 (ln (5) + ln (7))

Frequently Asked Questions (FAQ)

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