What is the answer to 14.47=(x-11)/(ln(x/(11))) ?

The answer to 14.47=(x-11)/(ln(x/(11))) is x=-(1447\W_{-1}(-\frac{1100)/(1447e^{1100/1447)})}{100}

Solve for x: 14.47=(x-11)/(ln(x/(11)))

The solution is x=-(1447\W_{-1}(-\frac{1100)/(1447e^{1100/1447)})}{100}

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14.47 = \frac{x - 11}{ln ( \frac{x}{11} )}

x = - \frac{1447 W _{- 1} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}

Decimal

x = 18.60271 \dots

Solution steps

14.47 = \frac{x - 11}{ln ( \frac{x}{11} )}

Multiply both sides by

ln (\frac{x}{11})

14.47 ln (\frac{x}{11}) = x - 11

Multiply both sides by

100

1447 ln (\frac{x}{11}) = 100 x - 1100

Divide both sides by

1447

ln (\frac{x}{11}) = \frac{100 x - 1100}{1447}

f (x) = g (x),

then

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

e^{l n (\frac{x}{11})} = e^{\frac{100 x - 1100}{1447}}

Simplify

e^{l n (\frac{x}{11})} : \frac{x}{11}

\frac{x}{11} = e^{\frac{100 x - 1100}{1447}}

Multiply both sides by

11

\frac{x}{11} \cdot 11 = e^{\frac{100 x - 1100}{1447}} \cdot 11

Simplify

x = e^{\frac{100 x - 1100}{1447}} \cdot 11

Solve

x = e^{\frac{100 x - 1100}{1447}} \cdot 11 : x = - \frac{1447 W _{- 1} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}, x = - \frac{1447 W _{0} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}

x = - \frac{1447 W _{- 1} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}, x = - \frac{1447 W _{0} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}

Verify Solutions:

x = - \frac{1447 W _{- 1} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}

True

, x = - \frac{1447 W _{0} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}

False

The solution is

x = - \frac{1447 W _{- 1} ( - \frac{1100}{1447 e ^{\frac{1100}{1447}}} )}{100}

f, f^{- 1} (x) = ln (x)

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

- 20 = 10 \times lo g_{10} (x)

y, ∣ y ∣ = x

∣ 6 - 6 x ∣ = 19

What is the answer to 14.47=(x-11)/(ln(x/(11))) ?
The answer to 14.47=(x-11)/(ln(x/(11))) is x=-(1447\W_{-1}(-\frac{1100)/(1447e^{1100/1447)})}{100}
Solve for x: 14.47=(x-11)/(ln(x/(11)))
The solution is x=-(1447\W_{-1}(-\frac{1100)/(1447e^{1100/1447)})}{100}