What is the answer to ln(x+1)=2-2x ?

The answer to ln(x+1)=2-2x is x=(\W_{0}(2e^4)-2)/2

Solve for x: ln(x+1)=2-2x

The solution is x=(\W_{0}(2e^4)-2)/2

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ln (x + 1) = 2 - 2 x

x = \frac{W _{0} ( 2 e ^{4} ) - 2}{2}

Decimal

x = 0.72685 \dots

Solution steps

ln (x + 1) = 2 - 2 x

f (x) = g (x),

then

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

e^{l n (x + 1)} = e^{2 - 2 x}

Simplify

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

x + 1 = e^{2 - 2 x}

Solve

x + 1 = e^{2 - 2 x} : x = \frac{W _{0} ( 2 e ^{4} ) - 2}{2}

x = \frac{W _{0} ( 2 e ^{4} ) - 2}{2}

Verify Solutions:

x = \frac{W _{0} ( 2 e ^{4} ) - 2}{2}

True

The solution is

x = \frac{W _{0} ( 2 e ^{4} ) - 2}{2}

lo g_{16} (3 x + 1) = 2

ln^{2} (x) - ln (x) - 2 = 0

20 lo g_{10} (x) = 60

lo g_{5} (4) + lo g_{5} (x) = 0

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

What is the answer to ln(x+1)=2-2x ?
The answer to ln(x+1)=2-2x is x=(\W_{0}(2e^4)-2)/2
Solve for x: ln(x+1)=2-2x
The solution is x=(\W_{0}(2e^4)-2)/2