What is the answer to (ln(N))/N = 1/5 ?

The answer to (ln(N))/N = 1/5 is N=-5\W_{-1}(-1/5),N=-5\W_{0}(-1/5)

Solve for N: (ln(N))/N = 1/5

The solution is N=-5\W_{-1}(-1/5),N=-5\W_{0}(-1/5)

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\frac{ln ( N )}{N} = \frac{1}{5}

N = - 5 W_{- 1} (- \frac{1}{5}), N = - 5 W_{0} (- \frac{1}{5})

Decimal

N = 12.71320 \dots, N = 1.29585 \dots

Solution steps

\frac{ln ( N )}{N} = \frac{1}{5}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

ln (N) \cdot 5 = N \cdot 1

Simplify

ln (N) \cdot 5 = N

Divide both sides by

5

ln (N) = \frac{N}{5}

f (x) = g (x),

then

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

e^{l n (N)} = e^{\frac{N}{5}}

Simplify

e^{l n (N)} : N

N = e^{\frac{N}{5}}

Solve

N = e^{\frac{N}{5}} : N = - 5 W_{- 1} (- \frac{1}{5}), N = - 5 W_{0} (- \frac{1}{5})

N = - 5 W_{- 1} (- \frac{1}{5}), N = - 5 W_{0} (- \frac{1}{5})

Verify Solutions:

N = - 5 W_{- 1} (- \frac{1}{5})

True

, N = - 5 W_{0} (- \frac{1}{5})

True

The solutions are

N = - 5 W_{- 1} (- \frac{1}{5}), N = - 5 W_{0} (- \frac{1}{5})

2 = lo g_{10} (x)

x, 20 + 47 lo g_{10} (x + 2) = 65

2 lo g_{10} (x) = lo g_{10} (2 x - 3) + lo g_{10} (3)

lo g_{d} (3) = \frac{1}{2}

lo g_{10} (x) + lo g_{10} (x - 5) = lo g_{10} (6)

What is the answer to (ln(N))/N = 1/5 ?
The answer to (ln(N))/N = 1/5 is N=-5\W_{-1}(-1/5),N=-5\W_{0}(-1/5)
Solve for N: (ln(N))/N = 1/5
The solution is N=-5\W_{-1}(-1/5),N=-5\W_{0}(-1/5)