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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

x ln (e) = x

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

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Frequently Asked Questions (FAQ)

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