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Popular >

simplify ln((e^{2x})/x)

Solution

simplify

ln (\frac{e ^{2 x}}{x})

Solution

2 x - ln (x)

Solution steps

ln (\frac{e ^{2 x}}{x})

Apply log rule:

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

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

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

Apply log rule:

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

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

= 2 x ln (e) - ln (x)

2 x ln (e) = 2 x

= 2 x - ln (x)

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Frequently Asked Questions (FAQ)

What is ln((e^{2x})/x) ?
The solution to ln((e^{2x})/x) is 2x-ln(x)