What is the answer to ln(1-x)= 10/3 x-4.16 ?

The answer to ln(1-x)= 10/3 x-4.16 is x=-(\W_{0}(\frac{3.33333…)/(e^{0.82666…)})-3.33333…}{3.33333…}

Solve for x: ln(1-x)= 10/3 x-4.16

The solution is x=-(\W_{0}(\frac{3.33333…)/(e^{0.82666…)})-3.33333…}{3.33333…}

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ln (1 - x) = \frac{10}{3} x - 4.16

x = - \frac{W _{0} ( \frac{3.33333 \dots}{e ^{0.82666 \dots}} ) - 3.33333 \dots}{3.33333 \dots}

Decimal

x = 0.78577 \dots

Solution steps

ln (1 - x) = \frac{10}{3} x - 4.16

f (x) = g (x),

then

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

e^{l n (1 - x)} = e^{\frac{10}{3} x - 4.16}

Simplify

e^{l n (1 - x)} : 1 - x

1 - x = e^{\frac{10}{3} x - 4.16}

Simplify

1 - x = e^{3.33333 \dots x - 4.16}

Solve

1 - x = e^{3.33333 \dots x - 4.16} : x = - \frac{W _{0} ( \frac{3.33333 \dots}{e ^{0.82666 \dots}} ) - 3.33333 \dots}{3.33333 \dots}

x = - \frac{W _{0} ( \frac{3.33333 \dots}{e ^{0.82666 \dots}} ) - 3.33333 \dots}{3.33333 \dots}

Verify Solutions:

x = - \frac{W _{0} ( \frac{3.33333 \dots}{e ^{0.82666 \dots}} ) - 3.33333 \dots}{3.33333 \dots}

True

The solution is

x = - \frac{W _{0} ( \frac{3.33333 \dots}{e ^{0.82666 \dots}} ) - 3.33333 \dots}{3.33333 \dots}

lo g_{2} (x - 3) = 0

lo g_{x} (2 x^{2} - 9 x + 14) = 2

lo g_{10} (5 - 2 x) = 1

lo g_{4} (10 + 2 x) = 3

lo g_{x + 7} (5 x + 5) = 3

What is the answer to ln(1-x)= 10/3 x-4.16 ?
The answer to ln(1-x)= 10/3 x-4.16 is x=-(\W_{0}(\frac{3.33333…)/(e^{0.82666…)})-3.33333…}{3.33333…}
Solve for x: ln(1-x)= 10/3 x-4.16
The solution is x=-(\W_{0}(\frac{3.33333…)/(e^{0.82666…)})-3.33333…}{3.33333…}