What is the answer to x=-ln(x-2) ?

The answer to x=-ln(x-2) is x=\W_{0}(1/(e^2))+2

Solve for x: x=-ln(x-2)

The solution is x=\W_{0}(1/(e^2))+2

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x = - ln (x - 2)

x = W_{0} (\frac{1}{e ^{2}}) + 2

Decimal Notation

x = 2.12002 \dots

Solution steps

x = - ln (x - 2)

Move

ln (x - 2)

to the left side

x + ln (x - 2) = 0

Move

x

to the right side

ln (x - 2) = - x

f (x) = g (x),

then

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

e^{l n (x - 2)} = e^{- x}

Simplify

e^{l n (x - 2)} : x - 2

x - 2 = e^{- x}

Solve

x - 2 = e^{- x} : x = W_{0} (\frac{1}{e ^{2}}) + 2

x = W_{0} (\frac{1}{e ^{2}}) + 2

Verify Solutions:

x = W_{0} (\frac{1}{e ^{2}}) + 2

True

The solution is

x = W_{0} (\frac{1}{e ^{2}}) + 2

lo g_{10} (2565 x) = 7

2 = ln (3 + c)

p (a) (a - b (a) ln (p (a))) = 0

3 = 10 \cdot lo g_{10} (x)

10 lo g_{8} (x) = 5

What is the answer to x=-ln(x-2) ?
The answer to x=-ln(x-2) is x=\W_{0}(1/(e^2))+2
Solve for x: x=-ln(x-2)
The solution is x=\W_{0}(1/(e^2))+2