What is the answer to x-2=log_{e}(x) ?

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

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x-2=log_{e}(x)

x - 2 = lo g_{e} (x)

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

Decimal

x = 3.14619 \dots, x = 0.15859 \dots

Solution steps

x - 2 = lo g_{e} (x)

f (x) = g (x),

then

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

e^{x - 2} = e^{l o g_{e} (x)}

Simplify

e^{l o g_{e} (x)} : x

e^{x - 2} = x

Solve

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

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

Verify Solutions:

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

True

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

True

The solutions are

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

y, x = 2 ln (3 - y)

5 ln (x) + 5 = 0

ln (x + 1 - \frac{x}{4}) = 0

\frac{1}{5} lo g_{10} (x + 2) - 1 = 0

lo g_{10} (6 x) = 216

What is the answer to x-2=log_{e}(x) ?
The answer to x-2=log_{e}(x) is x=-\W_{-1}(-1/(e^2)),x=-\W_{0}(-1/(e^2))