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Popular >

simplify ln((e^x)/x)

Solution

simplify

ln (\frac{e ^{x}}{x})

Solution

x - ln (x)

Solution steps

ln (\frac{e ^{x}}{x})

Apply log rule:

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

ln (\frac{e ^{x}}{x}) = ln (e^{x}) - ln (x)

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

Apply log rule:

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

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

= x ln (e) - ln (x)

x ln (e) = x

= x - ln (x)

Popular Examples

simplify log_{b}(7*3)simplify

lo g_{b} (7 \cdot 3)

simplify-log_{10}(4.3*10^{-4})simplify

- lo g_{10} (4.3 \cdot 1 0^{- 4})

simplify log_{8}(64x^4)simplify

lo g_{8} (64 x^{4})

expand log_{12}((12)/y)expand

lo g_{12} (\frac{12}{y})

simplify-(5/8)log_{2}(5/8)-(3/8)log_{2}(3/8)simplify

- (\frac{5}{8}) lo g_{2} (\frac{5}{8}) - (\frac{3}{8}) lo g_{2} (\frac{3}{8})

Frequently Asked Questions (FAQ)

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