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Popular >

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

Solution

simplify

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

Solution

ln (x) + x ln (x - 1)

Solution steps

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

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

Apply log rule:

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

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

= ln (x) + x ln (x - 1)

Popular Examples

simplify 0.796+0.05916log_{10}(1.587*10^{-6})simplify

0.796 + 0.05916 lo g_{10} (1.587 \cdot 1 0^{- 6})

simplify ln(1/11)simplify

ln (\frac{1}{11})

simplify ln(8)-ln(16)simplify

ln (8) - ln (16)

simplify-log_{10}(2.72*10^{-6})simplify

- lo g_{10} (2.72 \cdot 1 0^{- 6})

simplify ln(4sqrt(2))+i(45+2kpi)simplify

ln (42) + i (4 5^{\circ} + 2 kπ)

Frequently Asked Questions (FAQ)

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