What is the answer to ln(x)=x-3 ?

The answer to ln(x)=x-3 is x=-\W_{-1}(-1/(e^3)),x=-\W_{0}(-1/(e^3))

Solve for x: ln(x)=x-3

The solution is x=-\W_{-1}(-1/(e^3)),x=-\W_{0}(-1/(e^3))

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ln (x) = x - 3

x = - W_{- 1} (- \frac{1}{e ^{3}}), x = - W_{0} (- \frac{1}{e ^{3}})

Decimal Notation

x = 4.50524 \dots, x = 0.05246 \dots

Solution steps

ln (x) = x - 3

f (x) = g (x),

then

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

e^{l n (x)} = e^{x - 3}

Simplify

e^{l n (x)} : x

x = e^{x - 3}

Solve

x = e^{x - 3} : x = - W_{- 1} (- \frac{1}{e ^{3}}), x = - W_{0} (- \frac{1}{e ^{3}})

x = - W_{- 1} (- \frac{1}{e ^{3}}), x = - W_{0} (- \frac{1}{e ^{3}})

Verify Solutions:

x = - W_{- 1} (- \frac{1}{e ^{3}})

True

, x = - W_{0} (- \frac{1}{e ^{3}})

True

The solutions are

x = - W_{- 1} (- \frac{1}{e ^{3}}), x = - W_{0} (- \frac{1}{e ^{3}})

lo g_{e} (x - 1) - 1 = 0

4 lo g_{9} (x) - 9 lo g_{27} (7) = 14

5 = \frac{lo g _{10} ( x )}{3} + 3

4 lo g_{10} (x - 1) (2 x - 1) = 0

lo g_{10} (x) = 12.449

What is the answer to ln(x)=x-3 ?
The answer to ln(x)=x-3 is x=-\W_{-1}(-1/(e^3)),x=-\W_{0}(-1/(e^3))
Solve for x: ln(x)=x-3
The solution is x=-\W_{-1}(-1/(e^3)),x=-\W_{0}(-1/(e^3))