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Popular >

-6x=ln|1-4x|

Solution

- 6 x = ln ∣ 1 - 4 x ∣

Solution

x = \frac{2 W _{- 1} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12}, x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12}, x = \frac{2 W _{0} ( \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12}

+1

Decimal Notation

x = 0, x = 0.14570 \dots, x = 0.29307 \dots

Solution steps

- 6 x = ln ∣ 1 - 4 x ∣

If

f (x) = g (x),

then

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

e^{- 6 x} = e^{l n ∣ 1 - 4 x ∣}

Simplify

e^{l n ∣ 1 - 4 x ∣} : ∣ 1 - 4 x ∣

e^{- 6 x} = ∣ 1 - 4 x ∣

Solve

e^{- 6 x} = ∣ 1 - 4 x ∣ : x = \frac{2 W _{- 1} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12} or x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12} or x = \frac{2 W _{0} ( \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12}

x = \frac{2 W _{- 1} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12} or x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12} or x = \frac{2 W _{0} ( \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12}

Verify Solutions:

x = \frac{2 W _{- 1} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12}

True

, x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12}

True

, x = \frac{2 W _{0} ( \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12}

True

The solutions are

x = \frac{2 W _{- 1} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12}, x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12}, x = \frac{2 W _{0} ( \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{12}

Popular Examples

log_{10}(33)+log_{10}(x)=35

lo g_{10} (33) + lo g_{10} (x) = 35

4 + ln (x) = 2.0706

ln(2x)+ln(3x)=15

ln (2 x) + ln (3 x) = 15

14log_{10}(x^2-x-6)=1

14 lo g_{10} (x^{2} - x - 6) = 1

2log_{10}(x+2)=x

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

Frequently Asked Questions (FAQ)

What is the answer to -6x=ln|1-4x| ?
The answer to -6x=ln|1-4x| is
Solve for x: -6x=ln|1-4x|
The solution is