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Popular >

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

Solution

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

Solution

x = ln (\frac{1 + 5}{2})

+1

Solution steps

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

If

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{l n (e^{- x} + 1)} = e^{x}

Simplify

e^{l n (e^{- x} + 1)} : e^{- x} + 1

e^{- x} + 1 = e^{x}

Solve

e^{- x} + 1 = e^{x} : x = ln (\frac{1 + 5}{2})

x = ln (\frac{1 + 5}{2})

Verify Solutions:

x = ln (\frac{1 + 5}{2})

True

The solution is

x = ln (\frac{1 + 5}{2})

Popular Examples

x = 8 \cdot lo g_{2} (x)

ln(x)=6.377125338

ln (x) = 6.377125338

log_{9}(x-17)=2

lo g_{9} (x - 17) = 2

ln(x)+ln(1+2x)=ln(15)

ln (x) + ln (1 + 2 x) = ln (15)

5 lo g_{10} (x) = 5

Frequently Asked Questions (FAQ)

What is the answer to ln(e^{-x}+1)=x ?
The answer to ln(e^{-x}+1)=x is x=ln((1+sqrt(5))/2)